Question 1

Solve the system using the inverse method.
-$$\left\{ \begin{aligned}
x + 3 y & = - 8 \
21 x + 6 y & = 3
\end{aligned} \right.$$

Accepted Answer

A)  $x = - 3 , y = 1$ 
B)  $x = 1 , y = - 3$ 
C)  $x = - 1 , y = 3$ 
D)  $x = 3 , y = - 1$ 
A)  $x = - 3 , y = 1$ 
B)  $x = 1 , y = - 3$ 
C)  $x = - 1 , y = 3$ 
D)  $x = 3 , y = - 1$

Question 2

Perform the row operation(s) on the given augmented matrix.
-$$\begin{array} { l } 
\mathrm { R } _ { 2 } = - 4 \mathrm { r } _ { 1 } \
{ \left[ \begin{array} { l l | l } 
1 & 7 & 10 \
4 & 8 & - 4
\end{array} \right] }
\end{array}$$

Accepted Answer

A)  $\left[ \begin{array} { r r | r } - 4 & - 28 & - 40 \ 0 & - 20 & - 44 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 1 & 3 & 10 \ 0 & 10 & 18 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r | r } - 4 & - 28 & - 40 \ 4 & 8 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } 1 & 7 & 10 \ 0 & - 20 & - 44 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r | r } - 4 & - 28 & - 40 \ 0 & - 20 & - 44 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 1 & 3 & 10 \ 0 & 10 & 18 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r | r } - 4 & - 28 & - 40 \ 4 & 8 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } 1 & 7 & 10 \ 0 & - 20 & - 44 \end{array} \right]$

Question 3

Solve the system of equations.
-$$\left\{ \begin{array} { c } 
x + y + z = 7 \
x - y + 2 z = 7 \
5 x + y + z = 11
\end{array} \right.$$

Accepted Answer

A)  $x = 1 , y = 4 , z = 2$ 
B)  $x = 4 , y = 2 , z = 1$ 
C)  $x = 1 , y = 2 , z = 4$ 
D)  $x = 4 , y = 1 , z = 2$ 
A)  $x = 1 , y = 4 , z = 2$ 
B)  $x = 4 , y = 2 , z = 1$ 
C)  $x = 1 , y = 2 , z = 4$ 
D)  $x = 4 , y = 1 , z = 2$

Question 4

Graph the inequality.
-$x^{2}+y^{2}>16$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 5

Write the system of equations associated with the augmented matrix. Do not solve.
-$$\left[ \begin{array} { r r r | r } 
1 & 0 & 0 & - 8 \
0 & 1 & 0 & - 6 \
0 & 0 & 1 & - 10
\end{array} \right]$$

Accepted Answer

A)  $\left\{ \begin{array} { l } x = 0 \ y = - 14 \ z = - 18 \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } x = 15 \ y = 1 \ z = 0 \end{array} \right.$ 
C)  $\left\{ \begin{array} { l } x = - 9 \ y = 5 \ z = 6 \end{array} \right.$ 
D)  $\left\{ \begin{array} { l } x = - 8 \ y = - 6 \ z = - 10 \end{array} \right.$ 
A)  $\left\{ \begin{array} { l } x = 0 \ y = - 14 \ z = - 18 \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } x = 15 \ y = 1 \ z = 0 \end{array} \right.$ 
C)  $\left\{ \begin{array} { l } x = - 9 \ y = 5 \ z = 6 \end{array} \right.$ 
D)  $\left\{ \begin{array} { l } x = - 8 \ y = - 6 \ z = - 10 \end{array} \right.$

Question 6

Solve the system.
-$$\left\{ \begin{array} { l } 
x + y = 1 \
x + y = - 3
\end{array} \right.$$

Accepted Answer

A)  inconsistent (no solution) 
B)  $( 0 , - 2 )$ 
C)  dependent (many solutions) 
D)  $( 1 , - 3 )$ 
A)  inconsistent (no solution) 
B)  $( 0 , - 2 )$ 
C)  dependent (many solutions) 
D)  $( 1 , - 3 )$

Question 7

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-The equation of the line passing through the distinct points $\left( x _ { 1 } , y _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } \right)$ is given by $\left| \begin{array} { l l l } x _ { 1 } & y & 1 \ x _ { 1 } & y _ { 1 } & 1 \ x _ { 2 } & y _ { 2 } & 1 \end{array} \right| = 0 .$
Find the equation of the line passing through the points $( 3,5 )$ and $( - 1,4 )$.

Accepted Answer

A)  $x + 4 y + 17 = 0$ 
B)  $- x + 4 y - 17 = 0$ 
C)  $x + 7 y + 17 = 0$ 
D)  $x - 4 y + 17 = 0$ 
A)  $x + 4 y + 17 = 0$ 
B)  $- x + 4 y - 17 = 0$ 
C)  $x + 7 y + 17 = 0$ 
D)  $x - 4 y + 17 = 0$

Question 8

Solve the problem.
-The sum of the squares of two numbers is 5. The difference of the two numbers is 1. Find the two numbers.

Accepted Answer

A)  -2 and -1 
B)  -2 and -1; or 1 and 2 
C)  -2 and 1; or -1 and 2 
D)  1 and 2 
A)  -2 and -1 
B)  -2 and -1; or 1 and 2 
C)  -2 and 1; or -1 and 2 
D)  1 and 2

Question 9

Find the value(s) of the function, subject to the system of inequalities.
-Find the maximum and minimum of $z = 18 x + 24 y$ subject to $x \geq 0 , y \geq 0,4 x + 5 y \leq 30,4 x + 3 y \leq 20 , x \leq 5 , y \leq 8$

Accepted Answer

A)  $- 144 ; 0$ 
B)  $- 97.5 ; - 144$ 
C)  $90 ; 0$ 
D)  $90 ; - 144$ 
A)  $- 144 ; 0$ 
B)  $- 97.5 ; - 144$ 
C)  $90 ; 0$ 
D)  $90 ; - 144$

Question 10

Choose the one alternative that best completes the statement or answers the question.
-A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100. The camp can
Accommodate up to 45 staff members and needs at least 30 to run properly. They must have at least 10 aides,
And may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the
Camp hire to minimize cost?

Accepted Answer

A)  35 counselors and 10 aides 
B)  12 counselors and 18 aides 
C)  27 counselors and 18 aides 
D)  18 counselors and 12 aides 
A)  35 counselors and 10 aides 
B)  12 counselors and 18 aides 
C)  27 counselors and 18 aides 
D)  18 counselors and 12 aides

Question 11

Write the word or phrase that best completes each statement or answers the question.
-Find real numbers a, b, and c such that the graph of the function y = ax2 + bx + c contains the points (1, 1), (2, 4),
and (-3, 29).

Accepted Answer

a = 2, b =

Question 12

Perform the indicated operation, whenever possible.
-$$\left[ \begin{array} { r r } 
- 9 & - 9 \
- 8 & - 2 \
8 & 7
\end{array} \right] + \left[ \begin{array} { l l } 
5 & - 4 \
6 & - 2 \
2 & - 9
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { l l } - 4 & - 13 \ - 2 & - 4 \ 10 & - 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } - 4 & - 2 \ - 2 & - 4 \ 10 & - 2 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 14 & - 5 \ - 14 & 0 \ 6 & 13 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 4 & - 13 \ 2 & - 2 \ 10 & 2 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l } - 4 & - 13 \ - 2 & - 4 \ 10 & - 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } - 4 & - 2 \ - 2 & - 4 \ 10 & - 2 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 14 & - 5 \ - 14 & 0 \ 6 & 13 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 4 & - 13 \ 2 & - 2 \ 10 & 2 \end{array} \right]$

Question 13

Graph the inequality.
-$x>2$

Accepted Answer

A) 
  
B) 
  
C)  
  
D) 
  
A) 
  
B) 
  
C)  
  
D)

Question 14

Find the maximum or minimum value of the objective function, subject to the constraints graphed in this feasible region.  
-$= x + 8 y .$ Find maximum.

Accepted Answer

A)  Maximum 27 
B)  Maximum 34 
C)  Maximum 20 
D)  Maximum 42 
A)  Maximum 27 
B)  Maximum 34 
C)  Maximum 20 
D)  Maximum 42

Question 15

Graph the inequality.
-$x-y<-2$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 16

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
-$$\begin{array} { l } 
x + 3 y - 2 z - w = 27 \
4 x + y + z + 2 w = 14 \
- 3 x - y - 3 z - 2 w = - 1 \
x - y - 3 z - 2 w = 11
\end{array}$$

Accepted Answer

A)  $\{ ( 27,14 , - 1,11 ) \}$ 
B)  $\{ ( 3,5 , - 5,1 ) \}$ 
C)  $\{ ( 2,7 , - 9,3 ) \}$ 
D)  $\{ ( 3 + w , 5 - 2 w , - 5 + 2 w , w ) \}$ 
A)  $\{ ( 27,14 , - 1,11 ) \}$ 
B)  $\{ ( 3,5 , - 5,1 ) \}$ 
C)  $\{ ( 2,7 , - 9,3 ) \}$ 
D)  $\{ ( 3 + w , 5 - 2 w , - 5 + 2 w , w ) \}$

Question 17

Choose the one alternative that best completes the statement or answers the question.
-$$\left\{ \begin{array} { l } 
2 x ^ { 2 } + x y - y ^ { 2 } = 3 \
x ^ { 2 } + 2 x y + y ^ { 2 } = 3
\end{array} \right.$$

Accepted Answer

A)  $x = - \frac { 2 } { 3 } , y = \frac { 1 } { 3 } ; x = \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { 1 } { 3 }$ 
B)  $x = \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { \sqrt { 3 } } { 3 } ; x = - \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { \sqrt { 3 } } { 3 }$ 
C)  $x = - \frac { 2 } { 3 } , y = - \frac { 1 } { 3 } ; x = \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { 1 } { 3 }$ 
D)  $x = \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { \sqrt { 3 } } { 3 } ; x = - \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { \sqrt { 3 } } { 3 }$ 
A)  $x = - \frac { 2 } { 3 } , y = \frac { 1 } { 3 } ; x = \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { 1 } { 3 }$ 
B)  $x = \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { \sqrt { 3 } } { 3 } ; x = - \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { \sqrt { 3 } } { 3 }$ 
C)  $x = - \frac { 2 } { 3 } , y = - \frac { 1 } { 3 } ; x = \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { 1 } { 3 }$ 
D)  $x = \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { \sqrt { 3 } } { 3 } ; x = - \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { \sqrt { 3 } } { 3 }$

Question 18

Solve the system using the inverse method.
-$$\left\{ \begin{array} { l } 
2 x + 6 y = 2 \
2 x - y = - 5
\end{array} \right.$$

Accepted Answer

A)  $x = - 1 , y = 2$ 
B)  $x = - 2 , y = 1$ 
C)  $x = 1 , y = - 2$ 
D)  $x = 2 , y = - 1$ 
A)  $x = - 1 , y = 2$ 
B)  $x = - 2 , y = 1$ 
C)  $x = 1 , y = - 2$ 
D)  $x = 2 , y = - 1$

Question 19

Write the system of equations associated with the augmented matrix. Do not solve.
-$$\left[ \begin{array} { r r | r } 
9 & - 5 & - 6 \
- 7 & - 2 & - 5
\end{array} \right]$$

Accepted Answer

A) $\left\{ \begin{array} { l } - 5 x + 9 y = - 6 \ - 7 x - 2 y = - 5 \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 9 x - 5 y = - 6 \ - 7 x - 2 y = - 5 \end{array} \right.$ 
C)  $\left\{ \begin{array} { c } 9 x - 5 y = 0 \ - 7 x - 2 y = 0 \end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 9 x - 5 y = - 6 \ - 2 x - 7 y = - 5 \end{array} \right.$ 
A) $\left\{ \begin{array} { l } - 5 x + 9 y = - 6 \ - 7 x - 2 y = - 5 \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 9 x - 5 y = - 6 \ - 7 x - 2 y = - 5 \end{array} \right.$ 
C)  $\left\{ \begin{array} { c } 9 x - 5 y = 0 \ - 7 x - 2 y = 0 \end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 9 x - 5 y = - 6 \ - 2 x - 7 y = - 5 \end{array} \right.$

Question 20

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the
systems of equations. Are the points of intersection solutions to the system of equations (Y/N)?
-

$$\begin{array} { l } 
2 x ^ { 2 } = y + 5 \
y = - 10 x + 3
\end{array}$$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Solve the system using the inverse method. - $\left\{ \begin{aligned}x + 3 y & = - 8 \\21 x + 6 y & = 3\end{aligned} \right.$

Perform the row operation(s) on the given augmented matrix. - =-4 1 7 10 4 8 -4

Solve the system of equations. - $\left\{ \begin{array} { c } x + y + z = 7 \\x - y + 2 z = 7 \\5 x + y + z = 11\end{array} \right.$

Graph the inequality. - $x^{2}+y^{2}>16$ $Graph the inequality. - x^{2}+y^{2}>16$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r r | r } 1 & 0 & 0 & - 8 \\0 & 1 & 0 & - 6 \\0 & 0 & 1 & - 10\end{array} \right]$

Solve the system. - $\left\{ \begin{array} { l } x + y = 1 \\x + y = - 3\end{array} \right.$

Solve the problem. -The sum of the squares of two numbers is 5. The difference of the two numbers is 1. Find the two numbers.

Find the value(s) of the function, subject to the system of inequalities. -Find the maximum and minimum of $z = 18 x + 24 y$ subject to $x \geq 0 , y \geq 0,4 x + 5 y \leq 30,4 x + 3 y \leq 20 , x \leq 5 , y \leq 8$

Write the word or phrase that best completes each statement or answers the question. -Find real numbers a, b, and c such that the graph of the function y = ax2 + bx + c contains the points (1, 1), (2, 4), and (-3, 29).

Perform the indicated operation, whenever possible. - $\left[ \begin{array} { r r } - 9 & - 9 \\- 8 & - 2 \\8 & 7\end{array} \right] + \left[ \begin{array} { l l } 5 & - 4 \\6 & - 2 \\2 & - 9\end{array} \right]$

Graph the inequality. - $x>2$

Find the maximum or minimum value of the objective function, subject to the constraints graphed in this feasible region. - $= x + 8 y .$ Find maximum.

Graph the inequality. - $x-y<-2$

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. - x+3y-2z-w=27 4x+y+z+2w=14 -3x-y-3z-2w=-1 x-y-3z-2w=11

Choose the one alternative that best completes the statement or answers the question. - $\left\{ \begin{array} { l } 2 x ^ { 2 } + x y - y ^ { 2 } = 3 \\x ^ { 2 } + 2 x y + y ^ { 2 } = 3\end{array} \right.$

Solve the system using the inverse method. - $\left\{ \begin{array} { l } 2 x + 6 y = 2 \\2 x - y = - 5\end{array} \right.$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r | r } 9 & - 5 & - 6 \\- 7 & - 2 & - 5\end{array} \right]$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 10: Systems of Equations and Inequalities

Solve the system using the inverse method. - {x+3y=−821x+6y=3\left\{ \begin{aligned}x + 3 y & = - 8 \\21 x + 6 y & = 3\end{aligned} \right.{x+3y21x+6y​=−8=3​