Question 1

Find an objective function that has a minimum value at the indicated vertices A and D of the constraint region shown below.

Accepted Answer

A) Answer will vary. Sample answer is $z = 0$ 
B) Answer will vary. Sample answer is $z = 5 x + 6 y$ 
C) Answer will vary. Sample answer is $z = 6 x + 5 y$ . 
D) Answer will vary. Sample answer is $z = 5 y$ 
E) Answer will vary. Sample answer is $z = 6 x$ 
A) Answer will vary. Sample answer is $z = 0$ 
B) Answer will vary. Sample answer is $z = 5 x + 6 y$ 
C) Answer will vary. Sample answer is $z = 6 x + 5 y$ . 
D) Answer will vary. Sample answer is $z = 5 y$ 
E) Answer will vary. Sample answer is $z = 6 x$

Question 2

Maximize the object function $z = 2 x + y$ subject to the constraints $3 x + y \leq 15,4 x + 3 y \leq 30 , x \geq 0 , \text { and } y \geq 0$ .

Accepted Answer

A) The maximum value is 10 at $( 2,6 )$ . 
B) The maximum value is 4 at $( 1,2 )$ . 
C) The maximum value is 10 at $( 3,4 )$ . 
D) The maximum value is 12 at $( 3,6 )$ . 
E) The maximum value is 5 at $( 2,1 )$ . 
A) The maximum value is 10 at $( 2,6 )$ . 
B) The maximum value is 4 at $( 1,2 )$ . 
C) The maximum value is 10 at $( 3,4 )$ . 
D) The maximum value is 12 at $( 3,6 )$ . 
E) The maximum value is 5 at $( 2,1 )$ .

Question 3

Solve each system of equations by the substitution method. $7 x - y = 6$ $- x - 7 y = 3$

Accepted Answer

A)  $\left( - \frac { 39 } { 50 } , \frac { 27 } { 50 } \right)$ 
B)  $\left( \frac { 9 } { 10 } , - \frac { 3 } { 10 } \right)$ 
C)  $\left( \frac { 39 } { 50 } , - \frac { 27 } { 50 } \right)$ 
D)  $\left( \frac { 9 } { 16 } , - \frac { 13 } { 16 } \right)$ 
E) no solution 
A)  $\left( - \frac { 39 } { 50 } , \frac { 27 } { 50 } \right)$ 
B)  $\left( \frac { 9 } { 10 } , - \frac { 3 } { 10 } \right)$ 
C)  $\left( \frac { 39 } { 50 } , - \frac { 27 } { 50 } \right)$ 
D)  $\left( \frac { 9 } { 16 } , - \frac { 13 } { 16 } \right)$ 
E) no solution

Question 4

A farming cooperative mixes two brands of cattle feed. Brand X costs $30 per bag, and brand Y costs $25 per bag. Research and available resources have indicated the following constraints. Brand X contains two units nutritional element A, two units of element B, and two units of element C.
Brand Y contains one unit of nutritional element A, nine units of element B, and three units of element C.
The minimum requirements for nutrients A, B, and C are 12 units, 36 units, and 24 units, respectively.
What is the optimal number of bags of each brand that should be mixed? What is optimal cost?

Accepted Answer

A) To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $540. 
B) To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $320. 
C) To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $240. 
D) To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $300. 
E) To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $360. 
A) To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $540. 
B) To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $320. 
C) To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $240. 
D) To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $300. 
E) To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $360.

Question 5

A company makes two models of doghouses. The times (in hours) required for assembling, painting, and packaging are shown in the table. $\begin{array} { l l l } 
\text { Process } & \text { Model A } & \text { Model B } \
\text { Assembling } & 2.5 & 3 \
\text { Painting } & 2 & 1 \
\text { Packaging } & 0.75 & 1.25
\end{array}$ The total times available for assembling, Painting, and packaging are 4000 hours, 2500 hours, and 1500 hours, respectively. The profits per unit are $60 for model A and $75 for model B. what is the optimal production level for each model? What is the optimal profit?

Accepted Answer

A) The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $98,571. 
B) The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $98,535. 
C) The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $97,500. 
D) The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $90,000. 
E) The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $75,000. 
A) The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $98,571. 
B) The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $98,535. 
C) The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $97,500. 
D) The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $90,000. 
E) The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $75,000.

Question 6

Solve the system below by elimination if possible. Then state whether the system below is consistent or inconsistent. $$\left\{ \begin{array} { r } 
4 b + m = 0 \
- 8 b - 2 m = 3
\end{array} \right.$$

Accepted Answer

A) The system is consistent and its solution is $( - 5,3 )$ 
B) The system is consistent and its solution is $( 5,3 )$ 
C) The system is consistent and its solution is $( - 3,5 )$ 
D) The system is consistent and its solution is $( 3,5 )$ 
E) The system is inconsistent and no solution exists. 
A) The system is consistent and its solution is $( - 5,3 )$ 
B) The system is consistent and its solution is $( 5,3 )$ 
C) The system is consistent and its solution is $( - 3,5 )$ 
D) The system is consistent and its solution is $( 3,5 )$ 
E) The system is inconsistent and no solution exists.

Question 7

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints. (You should graph the feasible solutions on the grid below before you attempt to find the minimum and maximum values.) Objective function: $z = 6 x - 7 y$ Constraints: $$\left\{ \begin{array} { l } 
x \geq 0 \
y \geq 0 \
5 x + 4 y \leq 20 \
3 x + 2 y \leq 6
\end{array} \right.$$

Accepted Answer

A)  $\text { maximum } = 24 \text { at } ( 4,0 )$ 
B)  $\text { maximum } = 12 \text { at } ( 2,0 )$ 
C)  $\text { maximum } = 35 \text { at } ( 0,5 )$ 
D)  $\text { The maximum is unbounded. }$ 
E)  $\text { There is no maximum. The feasable solution set is empty. }$ 
A)  $\text { maximum } = 24 \text { at } ( 4,0 )$ 
B)  $\text { maximum } = 12 \text { at } ( 2,0 )$ 
C)  $\text { maximum } = 35 \text { at } ( 0,5 )$ 
D)  $\text { The maximum is unbounded. }$ 
E)  $\text { There is no maximum. The feasable solution set is empty. }$

Question 8

Find the least squares regression line y = ax + b for the points $\left( x _ { 1 } , y _ { 1 } \right) , \left( x _ { 2 } , y _ { 2 } \right) , \mathbf { K } , \left( x _ { n } , y _ { n } \right)$ by solving the system for a and b. $\begin{array} { r } 
n b + \left( \sum _ { i = 1 } ^ { n } x _ { i } \right) a = \left( \sum _ { i = 1 } ^ { n } y _ { i } \right) \\
\left( \sum _ { i = 1 } ^ { n } x _ { i } \right) b + \left( \sum _ { i = 1 } ^ { n } x _ { i } ^ { 2 } \right) a = \left( \sum _ { i = 1 } ^ { n } x _ { i } y _ { i } \right)
\end{array}$ Points: $( 1,13 ) , ( 3,15 ) , ( 6,18 ) , ( 6,19 )$ space

Accepted Answer

A) y = 11.81x + 1.11 
B) y = -1.09x + 11.81 
C) y = -4.30x - 7.24 
D) y = 1.11x + 11.81 
E) y = 4.01x - 7.24 
A) y = 11.81x + 1.11 
B) y = -1.09x + 11.81 
C) y = -4.30x - 7.24 
D) y = 1.11x + 11.81 
E) y = 4.01x - 7.24

Question 9

Solve the system by the method of substitution. $\left\{ \begin{array} { l } 
- \frac { 1 } { 2 } x + \frac { 1 } { 8 } y = 1 \\
- \frac { 1 } { 3 } x + \frac { 1 } { 6 } y = 1
\end{array} \right.$

Accepted Answer

A) (-1, -4) 
B) (4, -1) 
C) (-4, -1) 
D) (-1, 4) 
E) (1, -4) 
A) (-1, -4) 
B) (4, -1) 
C) (-4, -1) 
D) (-1, 4) 
E) (1, -4)

Question 10

Find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints. Objective function: $z = 3 x + 4 y$ Constraints: $$\left\{ \begin{array} { l } 
y \geq 0 \
x - y \geq - 2 \
2 x + 3 y \geq 6 \
5 x + 2 y \leq 25
\end{array} \right.$$

Accepted Answer

A)  $\text { minimum } = 0 \text { at } ( 0,0 ) ; \text { maximum } = 29 \text { at } ( 3,5 )$ 
B)  $\text { minimum } = 9 \text { at } ( 3,0 ) ; \text { maximum } = 15 \text { at } ( 5,0 )$ 
C)  $\text { minimum } = 8 \text { at } ( 0,2 ) ; \text { maximum } = 27 \text { at } ( 3,5 )$ 
D)  $\text { minimum } = - 11 \text { at } ( 3,5 ) ; \text { maximum } = 15 \text { at } ( 5,0 )$ 
E)  $\text { minimum } = 8 \text { at } ( 0,2 ) ; \text { maximum } = 29 \text { at } ( 3,5 )$ 
A)  $\text { minimum } = 0 \text { at } ( 0,0 ) ; \text { maximum } = 29 \text { at } ( 3,5 )$ 
B)  $\text { minimum } = 9 \text { at } ( 3,0 ) ; \text { maximum } = 15 \text { at } ( 5,0 )$ 
C)  $\text { minimum } = 8 \text { at } ( 0,2 ) ; \text { maximum } = 27 \text { at } ( 3,5 )$ 
D)  $\text { minimum } = - 11 \text { at } ( 3,5 ) ; \text { maximum } = 15 \text { at } ( 5,0 )$ 
E)  $\text { minimum } = 8 \text { at } ( 0,2 ) ; \text { maximum } = 29 \text { at } ( 3,5 )$

Question 11

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points $( 3,4 ) , ( 0,1 ) , ( 6,1 )$ .

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } - 6 x - 2 y + 1 = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - 3 x - y + 1 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 6 x - 2 y + 19 = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } - 6 x - 2 y - 9 = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } - 3 x - y - 9 = 0$ 
A)  $x ^ { 2 } + y ^ { 2 } - 6 x - 2 y + 1 = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - 3 x - y + 1 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 6 x - 2 y + 19 = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } - 6 x - 2 y - 9 = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } - 3 x - y - 9 = 0$

Question 12

Derive a set of inequalities to describe the region. Triangle: vertices at (0, 0), (3, 0), (3, 5)

Accepted Answer

A)  $\left\{ \begin{array} { l } 
y \leq \frac { 5 } { 3 } x \
y \geq 0 \
x \leq 3
\end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 
y \leq \frac { 5 } { 3 } x \
x \leq 3
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
y \geq \frac { 5 } { 3 } x \
y \geq 0 \
x \leq 3
\end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 
y \leq \frac { 5 } { 3 } x \
x \geq 0
\end{array} \right.$ 
E)  $\left\{ \begin{array} { l } 
y \leq \frac { 3 } { 5 } x \
y \geq 0 \
x \leq 3
\end{array} \right.$ 
A)  $\left\{ \begin{array} { l } 
y \leq \frac { 5 } { 3 } x \
y \geq 0 \
x \leq 3
\end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 
y \leq \frac { 5 } { 3 } x \
x \leq 3
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
y \geq \frac { 5 } { 3 } x \
y \geq 0 \
x \leq 3
\end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 
y \leq \frac { 5 } { 3 } x \
x \geq 0
\end{array} \right.$ 
E)  $\left\{ \begin{array} { l } 
y \leq \frac { 3 } { 5 } x \
y \geq 0 \
x \leq 3
\end{array} \right.$

Question 13

A real estate company borrows $700,000. Some of the money is borrowed at 5%, some at 9%, and some at 11% simple annual interest. How much is borrowed at the 5% rate when the total annual interest is $55,000 and the amount borrowed at 9% is the same as the amount borrowed at 11%?

Accepted Answer

A) $700,000 
B) $300,000 
C) $500,000 
D) $200,000 
E) $900,000 
A) $700,000 
B) $300,000 
C) $500,000 
D) $200,000 
E) $900,000

Question 14

Use a graphing utility to find the point(s) of intersection of the graphs. $\left\{ \begin{aligned}
y & = e ^ { x + 2 } \
x - y + 3 & = 0
\end{aligned} \right.$

Accepted Answer

A)  $( - 1 , - 2 )$ 
B)  $( - 1,2 )$ 
C)  $( - 2,1 )$ 
D)  $( - 2 , - 1 )$ 
E)  $( 1,2 )$ 
A)  $( - 1 , - 2 )$ 
B)  $( - 1,2 )$ 
C)  $( - 2,1 )$ 
D)  $( - 2 , - 1 )$ 
E)  $( 1,2 )$

Question 15

The costs to a store two models of Global Positioning System (GPS) receivers are $80 and $100. The $80 model yields a profit of $25 and the $100 model yields a profit of $30. Market tests and available resources indicate the following constraints. The merchant estimates that the total monthly demand will not be exceed 200 units.
The merchant does not want to invest more than $18,000 in GPS receiver inventory.
What is the optimal inventory level for each model what is optimal profit?

Accepted Answer

A) A maximum profit of $4500 occurs when 180 of each model of GPS receiver is sold. 
B) A maximum profit of $5000 occurs when 200 of each model of GPS receiver is sold. 
C) A maximum profit of $5400 occurs when 180 of each model of GPS receiver is sold. 
D) A maximum profit of $6000 occurs when 200 of each model of GPS receiver is sold. 
E) A maximum profit of $5500 occurs when 100 of each model of GPS receiver is sold. 
A) A maximum profit of $4500 occurs when 180 of each model of GPS receiver is sold. 
B) A maximum profit of $5000 occurs when 200 of each model of GPS receiver is sold. 
C) A maximum profit of $5400 occurs when 180 of each model of GPS receiver is sold. 
D) A maximum profit of $6000 occurs when 200 of each model of GPS receiver is sold. 
E) A maximum profit of $5500 occurs when 100 of each model of GPS receiver is sold.

Question 16

A furniture company produces tables and chairs. Each table requires 2.5 hours in the assembly center and 1.75 hours in the finishing center. Each chair requires 1 hour in the assembly center and 1.25 hours in the finishing center. The company's assembly center is available 16 hours per day, and its finishing center is available 12 hours per day. Let $x$ and $y$ be the number of tables and chairs produced per day, respectively. Find a system of inequalities describing all possible production levels.

Accepted Answer

A)  $\left\{ \begin{aligned}
x + 1.25 y & \leq 16 \
2.5 x + 1.75 y & \leq 12 \
x & \geq 0 \
y & \geq 0
\end{aligned} \right.$ 
B)  $\left\{ \begin{aligned}
1.75 x + 1.25 y & \leq 16 \
2.5 x + y & \leq 12 \
x & \geq 0 \
y & \geq 0
\end{aligned} \right.$ 
C)  $\left\{ \begin{aligned}
2.5 x + 1.25 y & \leq 16 \
x + 1.75 y & \leq 12 \
x & \geq 0 \
y & \geq 0
\end{aligned} \right.$ 
D)  $\left\{ \begin{aligned}
2.5 x + 1.75 y & \leq 16 \
x + 1.25 y & \leq 12 \
x & \geq 0 \
y & \geq 0
\end{aligned} \right.$ 
E)  $\left\{ \begin{aligned}
2.5 x + y & \leq 16 \
1.75 x + 1.25 y & \leq 12 \
x & \geq 0 \
y & \geq 0
\end{aligned} \right.$ 
A)  $\left\{ \begin{aligned}
x + 1.25 y & \leq 16 \
2.5 x + 1.75 y & \leq 12 \
x & \geq 0 \
y & \geq 0
\end{aligned} \right.$ 
B)  $\left\{ \begin{aligned}
1.75 x + 1.25 y & \leq 16 \
2.5 x + y & \leq 12 \
x & \geq 0 \
y & \geq 0
\end{aligned} \right.$ 
C)  $\left\{ \begin{aligned}
2.5 x + 1.25 y & \leq 16 \
x + 1.75 y & \leq 12 \
x & \geq 0 \
y & \geq 0
\end{aligned} \right.$ 
D)  $\left\{ \begin{aligned}
2.5 x + 1.75 y & \leq 16 \
x + 1.25 y & \leq 12 \
x & \geq 0 \
y & \geq 0
\end{aligned} \right.$ 
E)  $\left\{ \begin{aligned}
2.5 x + y & \leq 16 \
1.75 x + 1.25 y & \leq 12 \
x & \geq 0 \
y & \geq 0
\end{aligned} \right.$

Question 17

Solve the system by elimination. $\left\{ \begin{array} { c } 
6 x + 8 y = 1 \
- 4 x - 3 y = - 14
\end{array} \right.$

Accepted Answer

A)  $\left( 1 , - \frac { 5 } { 8 } \right)$ 
B)  $\left( 3 , \frac { 2 } { 3 } \right)$ 
C)  $\left( \frac { 109 } { 14 } , - \frac { 40 } { 7 } \right)$ 
D)  $\left( a , \frac { 1 - 6 a } { 8 } \right) \text { (dependent) }$ 
E) inconsistent 
A)  $\left( 1 , - \frac { 5 } { 8 } \right)$ 
B)  $\left( 3 , \frac { 2 } { 3 } \right)$ 
C)  $\left( \frac { 109 } { 14 } , - \frac { 40 } { 7 } \right)$ 
D)  $\left( a , \frac { 1 - 6 a } { 8 } \right) \text { (dependent) }$ 
E) inconsistent

Question 18

Solve the system by the method of elimination. $\left\{ \begin{aligned}
5 x - y & = 43 \
- 8 x - y & = - 74
\end{aligned} \right.$

Accepted Answer

A)  $( 3,50 )$ 
B)  $( 9,2 )$ 
C)  $\left( - \frac { 31 } { 13 } , - \frac { 1106 } { 13 } \right)$ 
D)  $\left( - 2 , \frac { 41 } { 5 } \right)$ 
E) inconsistent 
A)  $( 3,50 )$ 
B)  $( 9,2 )$ 
C)  $\left( - \frac { 31 } { 13 } , - \frac { 1106 } { 13 } \right)$ 
D)  $\left( - 2 , \frac { 41 } { 5 } \right)$ 
E) inconsistent

Question 19

Solve the system of linear equations. $\left\{ \begin{array} { c } 
x + y + z = - 2 \
x + y - 3 z = 6 \
- y + 7 z = - 7
\end{array} \right.$

Accepted Answer

A)  $( 6 , - 8,0 )$ 
B)  $( - 8,6,0 )$ 
C)  $( 7 , - 7 , - 2 )$ 
D)  $( - 7,7 , - 2 )$ 
E)  $( 10 , - 9 , - 3 )$ 
A)  $( 6 , - 8,0 )$ 
B)  $( - 8,6,0 )$ 
C)  $( 7 , - 7 , - 2 )$ 
D)  $( - 7,7 , - 2 )$ 
E)  $( 10 , - 9 , - 3 )$

Question 20

The sales of various types of lawn and garden items vary according to the season. At a certain home improvement store, the monthly sales H of garden hoses (hoses sold per month) declines from July to October whereas the monthly sales of lawn rakes R (rakes sold per month) increase during this same interval. The sales of these two items during the calendar months July-October are modeled by the equations: H(t) = 64 - 6t
R(t) = 17t - 97,
Where t is the month (t = 7 corresponds to July). In which month does the number of rakes sold equal the number of hoses sold?

Accepted Answer

A) August 
B) September 
C) October 
D) November 
E) July 
A) August 
B) September 
C) October 
D) November 
E) July

Find an objective function that has a minimum value at the indicated vertices A and D of the constraint region shown below.

Maximize the object function $z = 2 x + y$ subject to the constraints $3 x + y \leq 15,4 x + 3 y \leq 30 , x \geq 0 , \text { and } y \geq 0$ .

Solve each system of equations by the substitution method. $7 x - y = 6$ $- x - 7 y = 3$

Solve the system below by elimination if possible. Then state whether the system below is consistent or inconsistent. $\left\{ \begin{array} { r } 4 b + m = 0 \\- 8 b - 2 m = 3\end{array} \right.$

Solve the system by the method of substitution. $\left\{ \begin{array} { l } - \frac { 1 } { 2 } x + \frac { 1 } { 8 } y = 1 \\\\- \frac { 1 } { 3 } x + \frac { 1 } { 6 } y = 1\end{array} \right.$

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points $( 3,4 ) , ( 0,1 ) , ( 6,1 )$ .

Derive a set of inequalities to describe the region. Triangle: vertices at (0, 0), (3, 0), (3, 5)

A real estate company borrows $700,000. Some of the money is borrowed at 5%, some at 9%, and some at 11% simple annual interest. How much is borrowed at the 5% rate when the total annual interest is $55,000 and the amount borrowed at 9% is the same as the amount borrowed at 11%?

Use a graphing utility to find the point(s) of intersection of the graphs. $\left\{ \begin{aligned}y & = e ^ { x + 2 } \\x - y + 3 & = 0\end{aligned} \right.$

Solve the system by elimination. $\left\{ \begin{array} { c } 6 x + 8 y = 1 \\- 4 x - 3 y = - 14\end{array} \right.$

Solve the system by the method of elimination. $\left\{ \begin{aligned}5 x - y & = 43 \\- 8 x - y & = - 74\end{aligned} \right.$

Solve the system of linear equations. $\left\{ \begin{array} { c } x + y + z = - 2 \\x + y - 3 z = 6 \\- y + 7 z = - 7\end{array} \right.$

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Exam 6: Systems of Equations and Inequalities

Find an objective function that has a minimum value at the indicated vertices A and D of the constraint region shown below.

Maximize the object function z=2x+yz = 2 x + yz=2x+y subject to the constraints 3x+y≤15,4x+3y≤30,x≥0, and y≥03 x + y \leq 15,4 x + 3 y \leq 30 , x \geq 0 , \text { and } y \geq 03x+y≤15,4x+3y≤30,x≥0, and y≥0 .

Solve each system of equations by the substitution method. 7x−y=67 x - y = 67x−y=6 −x−7y=3- x - 7 y = 3−x−7y=3

Solve the system below by elimination if possible. Then state whether the system below is consistent or inconsistent. {4b+m=0−8b−2m=3\left\{ \begin{array} { r } 4 b + m = 0 \\- 8 b - 2 m = 3\end{array} \right.{4b+m=0−8b−2m=3​

Solve the system by the method of substitution. {−12x+18y=1−13x+16y=1\left\{ \begin{array} { l } - \frac { 1 } { 2 } x + \frac { 1 } { 8 } y = 1 \\\\- \frac { 1 } { 3 } x + \frac { 1 } { 6 } y = 1\end{array} \right.⎩⎨⎧​−21​x+81​y=1−31​x+61​y=1​

Find the equation of the circle x2+y2+Dx+Ey+F=0x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0x2+y2+Dx+Ey+F=0 that passes through the points (3,4),(0,1),(6,1)( 3,4 ) , ( 0,1 ) , ( 6,1 )(3,4),(0,1),(6,1) .

Derive a set of inequalities to describe the region. Triangle: vertices at (0, 0), (3, 0), (3, 5)

A real estate company borrows $700,000. Some of the money is borrowed at 5%, some at 9%, and some at 11% simple annual interest. How much is borrowed at the 5% rate when the total annual interest is $55,000 and the amount borrowed at 9% is the same as the amount borrowed at 11%?

Use a graphing utility to find the point(s) of intersection of the graphs. {y=ex+2x−y+3=0\left\{ \begin{aligned}y & = e ^ { x + 2 } \\x - y + 3 & = 0\end{aligned} \right.{yx−y+3​=ex+2=0​

Solve the system by elimination. {6x+8y=1−4x−3y=−14\left\{ \begin{array} { c } 6 x + 8 y = 1 \\- 4 x - 3 y = - 14\end{array} \right.{6x+8y=1−4x−3y=−14​

Solve the system by the method of elimination. {5x−y=43−8x−y=−74\left\{ \begin{aligned}5 x - y & = 43 \\- 8 x - y & = - 74\end{aligned} \right.{5x−y−8x−y​=43=−74​

Solve the system of linear equations. {x+y+z=−2x+y−3z=6−y+7z=−7\left\{ \begin{array} { c } x + y + z = - 2 \\x + y - 3 z = 6 \\- y + 7 z = - 7\end{array} \right.⎩⎨⎧​x+y+z=−2x+y−3z=6−y+7z=−7​

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Maximize the object function $z = 2 x + y$ subject to the constraints $3 x + y \leq 15,4 x + 3 y \leq 30 , x \geq 0 , \text { and } y \geq 0$ .

Solve each system of equations by the substitution method. $7 x - y = 6$ $- x - 7 y = 3$

Solve the system below by elimination if possible. Then state whether the system below is consistent or inconsistent. $\left\{ \begin{array} { r } 4 b + m = 0 \\- 8 b - 2 m = 3\end{array} \right.$

Solve the system by the method of substitution. $\left\{ \begin{array} { l } - \frac { 1 } { 2 } x + \frac { 1 } { 8 } y = 1 \\\\- \frac { 1 } { 3 } x + \frac { 1 } { 6 } y = 1\end{array} \right.$

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points $( 3,4 ) , ( 0,1 ) , ( 6,1 )$ .

Use a graphing utility to find the point(s) of intersection of the graphs. $\left\{ \begin{aligned}y & = e ^ { x + 2 } \\x - y + 3 & = 0\end{aligned} \right.$

Solve the system by elimination. $\left\{ \begin{array} { c } 6 x + 8 y = 1 \\- 4 x - 3 y = - 14\end{array} \right.$

Solve the system by the method of elimination. $\left\{ \begin{aligned}5 x - y & = 43 \\- 8 x - y & = - 74\end{aligned} \right.$

Solve the system of linear equations. $\left\{ \begin{array} { c } x + y + z = - 2 \\x + y - 3 z = 6 \\- y + 7 z = - 7\end{array} \right.$