Question 1

Solve the system of equations by the elimination method.
-$$\left\{ \begin{array} { r } 
- x - 2 y = - 8 \
- 9 x - 18 y = 2
\end{array} \right.$$

Accepted Answer

A)  $( 8,0 )$ 
B)  $( 0,4 )$ 
C)  $\{ ( x , y ) \mid - x - 2 y = - 8 \}$ 
D)  $\varnothing$ 
A)  $( 8,0 )$ 
B)  $( 0,4 )$ 
C)  $\{ ( x , y ) \mid - x - 2 y = - 8 \}$ 
D)  $\varnothing$

Question 2

Solve the problem.
-A company that manufactures boxes recently purchased $880 worth of new equipment to offer gift boxes to its customers. The cost of producing a package of gift boxes is $0.30 and it is sold for $1.40. Find the number of
Packages that must be sold for the company to break even.

Accepted Answer

A)  820 packages 
B)  353 packages 
C)  810 packages 
D)  800 packages 
A)  820 packages 
B)  353 packages 
C)  810 packages 
D)  800 packages

Question 3

Solve the system of linear equations using matrices.
-$$\left\{ \begin{aligned}
3 x - 9 y + 4 z & = - 32 \
- 9 x + 27 y - 12 z & = 96 \
9 x - 27 y + 12 z & = - 96
\end{aligned} \right.$$

Accepted Answer

A)  $\{ ( x , y , z ) \mid 9 x - 27 y + 12 z = - 32 \}$ 
B)  $( - 1,1 , - 5 )$ 
C)  $\{ ( x , y , z ) \mid 3 x - 9 y + 4 z = - 32 \}$ 
D)  $\varnothing$ 
A)  $\{ ( x , y , z ) \mid 9 x - 27 y + 12 z = - 32 \}$ 
B)  $( - 1,1 , - 5 )$ 
C)  $\{ ( x , y , z ) \mid 3 x - 9 y + 4 z = - 32 \}$ 
D)  $\varnothing$

Question 4

Solve the system of linear equations using matrices.
-$$\left\{ \begin{array} { l } 
4 x + 2 y = 2 \
4 x = - 8
\end{array} \right.$$

Accepted Answer

A)  $( - 2 , - 5 )$ 
B)  $( 5 , - 2 )$ 
C)  $( - 2,5 )$ 
D)  $\varnothing$ 
A)  $( - 2 , - 5 )$ 
B)  $( 5 , - 2 )$ 
C)  $( - 2,5 )$ 
D)  $\varnothing$

Question 5

Solve the system.
-$$\left\{ \begin{array} { l } 
\frac { x } { 4 } - \frac { y } { 3 } = 1 \
\frac { x } { 4 } - y = 3
\end{array} \right.$$

Accepted Answer

A)  $( 3,0 )$ 
B)  $( - 3,0 )$ 
C)  $( 0 , - 3 )$ 
D)  $( 0,3 )$ 
A)  $( 3,0 )$ 
B)  $( - 3,0 )$ 
C)  $( 0 , - 3 )$ 
D)  $( 0,3 )$

Question 6

Solve the problem.
-A real estate investor is examining a triangular plot of land. She measures each angle of the field. The sum of the first and second angles is 80° more than the measure of the third angle. If the measure of the third angle is subtracted from the measure of the second angle, the result is thrice the measure of the first angle. Find the measure of each angle

Accepted Answer

A)  First angle is $20 ^ { \circ }$, second angle is $110 ^ { \circ }$, third angle is $50 ^ { \circ }$ 
B)  First angle is $18 ^ { \circ }$, second angle is $110 ^ { \circ }$, third angle is $48 ^ { \circ }$ 
C)  First angle is $24 ^ { \circ }$, second angle is $112 ^ { \circ }$, third angle is $44 ^ { \circ }$ 
D)  First angle is $26 ^ { \circ }$, second angle is $106 ^ { \circ }$, third angle is $48 ^ { \circ }$ 
A)  First angle is $20 ^ { \circ }$, second angle is $110 ^ { \circ }$, third angle is $50 ^ { \circ }$ 
B)  First angle is $18 ^ { \circ }$, second angle is $110 ^ { \circ }$, third angle is $48 ^ { \circ }$ 
C)  First angle is $24 ^ { \circ }$, second angle is $112 ^ { \circ }$, third angle is $44 ^ { \circ }$ 
D)  First angle is $26 ^ { \circ }$, second angle is $106 ^ { \circ }$, third angle is $48 ^ { \circ }$

Question 7

Solve the system of equations.
-$$\left\{ \begin{array} { r r } 
9 x - 5 y = & 4 \
- 18 x + 10 y = & - 12
\end{array} \right.$$

Accepted Answer

A)  $\left( \frac { 9 } { 8 } , - \frac { 5 } { 8 } \right)$ 
B)  $( 2,3 )$ 
C)  $\{ ( x , y ) \mid 9 x - 5 y = 4 \}$ 
D)  $\varnothing$ 
A)  $\left( \frac { 9 } { 8 } , - \frac { 5 } { 8 } \right)$ 
B)  $( 2,3 )$ 
C)  $\{ ( x , y ) \mid 9 x - 5 y = 4 \}$ 
D)  $\varnothing$

Question 8

Use matrices to solve the system.
-$$\left\{ \begin{array} { l } 
2 x + y = 8 \
6 x + 3 y = 24
\end{array} \right.$$

Accepted Answer

A)  $( 5 , - 2 )$ 
B)  $\varnothing$ 
C)  $\{ ( x , y ) \mid 2 x + y = 8 \}$ 
D)  $( 0,8 )$ 
A)  $( 5 , - 2 )$ 
B)  $\varnothing$ 
C)  $\{ ( x , y ) \mid 2 x + y = 8 \}$ 
D)  $( 0,8 )$

Question 9

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
-At the break-even point both cost and revenue are what?

Accepted Answer

A)  $1500 
B)  $2700 
C)  $750 
D)  $2250 
A)  $1500 
B)  $2700 
C)  $750 
D)  $2250

Question 10

Solve the system of equations by the elimination method.
-$$\left\{ \begin{array} { l } 
- 3 x - 7 y = - 26 \
- 5 x + 4 y = 35
\end{array} \right.$$

Accepted Answer

A)  $( - 3,5 )$ 
B)  $( 3 , - 5 )$ 
C)  $( 3,5 )$ 
D)  $( - 3 , - 5 )$ 
A)  $( - 3,5 )$ 
B)  $( 3 , - 5 )$ 
C)  $( 3,5 )$ 
D)  $( - 3 , - 5 )$

Question 11

Graph the solution of the system of linear inequalities.
-$\left\{\begin{array}{r}
3 y-x \geq-3 \
x+y \geq-5 \
y \leq 2
\end{array}\right.$

Accepted Answer

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

Question 12

Graph the solution of the system of linear inequalities.
-$\left\{ \begin{array} { l } 
y \leq 3 x - 3 \
y > 2 x
\end{array} \right.$

Accepted Answer

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

Question 13

Solve.
-Two cars leave a city and head in the same direction. After 5 hours, the faster car is 15 miles ahead of the slower car. The slower car has traveled 230 miles. Find the speeds of the two cars.

Accepted Answer

A)  30 mph and 33 mph 
B)  46 mph and 49 mph 
C)  43 mph and 46 mph 
D)  48 mph and 51 mph 
A)  30 mph and 33 mph 
B)  46 mph and 49 mph 
C)  43 mph and 46 mph 
D)  48 mph and 51 mph

Question 14

Graph the solution of the system of linear inequalities.
-$\left\{\begin{array}{r}
x+2 y>-4 \
y \leq-4
\end{array}\right.$

Accepted Answer

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

Question 15

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
-$$\begin{array} { l } 
C ( x ) = 0.3 x + 1320 \
R ( x ) = 1.5 x
\end{array}$$

Accepted Answer

A)  1120 units 
B)  1110 units 
C)  1100 units 
D)  489 units 
A)  1120 units 
B)  1110 units 
C)  1100 units 
D)  489 units

Question 16

Solve the system of equations by the substitution method.
-$$\left\{ \begin{aligned}
3 x - 4 y & = 32 \
x & = - 4 y
\end{aligned} \right.$$

Accepted Answer

A)  $( - 8 , - 2 )$ 
B)  $( - 2,8 )$ 
C)  $( 8,2 )$ 
D)  $( 8 , - 2 )$ 
A)  $( - 8 , - 2 )$ 
B)  $( - 2,8 )$ 
C)  $( 8,2 )$ 
D)  $( 8 , - 2 )$

Question 17

Solve the problem.
-Dmitri needs 7 liters of a 22% solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the 7% solution and the other an unlimited
Supply of the 42% solution. How many liters of each solution should Dmitri use?

Accepted Answer

A)  7% solution: 3.5 liters; 42% solution: 3.5 liters 
B)  7% solution: 3 liters; 42% solution: 4 liters 
C)  7% solution: 4.5 liters; 42% solution: 2.5 liters 
D)  7% solution: 4 liters; 42% solution: 3 liters 
A)  7% solution: 3.5 liters; 42% solution: 3.5 liters 
B)  7% solution: 3 liters; 42% solution: 4 liters 
C)  7% solution: 4.5 liters; 42% solution: 2.5 liters 
D)  7% solution: 4 liters; 42% solution: 3 liters

Question 18

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l } 
\text { matrix consistent system of equations triple } \
\text { solution inconsistent element } \
\text { column }
\end{array}$$
-Two or more linear equations in two variables form a(n) .

Accepted Answer

A)  matrix 
B)  row 
C)  system of equations 
D)  solution 
A)  matrix 
B)  row 
C)  system of equations 
D)  solution

Question 19

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
-What is the profit when 796 binoculars are produced?

Accepted Answer

A)  $3092 
B)  $92 
C)  $4684 
D)  $1684 
A)  $3092 
B)  $92 
C)  $4684 
D)  $1684

Question 20

Solve the system of linear equations using matrices.
-$$\left\{ \begin{array} { l } 
2 x + y = 8 \
2 x + 5 y = - 8
\end{array} \right.$$

Accepted Answer

A)  $( - 4 , - 6 )$ 
B)  $( 6 , - 4 )$ 
C)  $( - 4,6 )$ 
D)  $\varnothing$ 
A)  $( - 4 , - 6 )$ 
B)  $( 6 , - 4 )$ 
C)  $( - 4,6 )$ 
D)  $\varnothing$

Solve the system of equations by the elimination method. - $\left\{ \begin{array} { r } - x - 2 y = - 8 \\- 9 x - 18 y = 2\end{array} \right.$

Solve the problem. -A company that manufactures boxes recently purchased $880 worth of new equipment to offer gift boxes to its customers. The cost of producing a package of gift boxes is $0.30 and it is sold for $1.40. Find the number of Packages that must be sold for the company to break even.

Solve the system of linear equations using matrices. - $\left\{ \begin{aligned}3 x - 9 y + 4 z & = - 32 \\- 9 x + 27 y - 12 z & = 96 \\9 x - 27 y + 12 z & = - 96\end{aligned} \right.$

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { l } 4 x + 2 y = 2 \\4 x = - 8\end{array} \right.$

Solve the system. - $\left\{ \begin{array} { l } \frac { x } { 4 } - \frac { y } { 3 } = 1 \\\frac { x } { 4 } - y = 3\end{array} \right.$

Solve the system of equations. - $\left\{ \begin{array} { r r } 9 x - 5 y = & 4 \\- 18 x + 10 y = & - 12\end{array} \right.$

Use matrices to solve the system. - $\left\{ \begin{array} { l } 2 x + y = 8 \\6 x + 3 y = 24\end{array} \right.$

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even. -At the break-even point both cost and revenue are what?

Solve the system of equations by the elimination method. - $\left\{ \begin{array} { l } - 3 x - 7 y = - 26 \\- 5 x + 4 y = 35\end{array} \right.$

Graph the solution of the system of linear inequalities. - $\left\{\begin{array}{r}3 y-x \geq-3 \\x+y \geq-5 \\y \leq 2\end{array}\right.$ $Graph the solution of the system of linear inequalities. - \left\{\begin{array}{r} 3 y-x \geq-3 \\ x+y \geq-5 \\ y \leq 2 \end{array}\right.$

Graph the solution of the system of linear inequalities. - $\left\{ \begin{array} { l } y \leq 3 x - 3 \\y > 2 x\end{array} \right.$ $Graph the solution of the system of linear inequalities. - \left\{ \begin{array} { l } y \leq 3 x - 3 \\ y > 2 x \end{array} \right.$

Solve. -Two cars leave a city and head in the same direction. After 5 hours, the faster car is 15 miles ahead of the slower car. The slower car has traveled 230 miles. Find the speeds of the two cars.

Graph the solution of the system of linear inequalities. - $\left\{\begin{array}{r}x+2 y>-4 \\y \leq-4\end{array}\right.$ $Graph the solution of the system of linear inequalities. - \left\{\begin{array}{r} x+2 y>-4 \\ y \leq-4 \end{array}\right.$

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even. - C(x)=0.3x+1320 R(x)=1.5x

Solve the system of equations by the substitution method. - $\left\{ \begin{aligned}3 x - 4 y & = 32 \\x & = - 4 y\end{aligned} \right.$

Fill in the blank with one of the words or phrases listed below. matrix consistent system of equations triple solution inconsistent element column -Two or more linear equations in two variables form a(n) .

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even. -What is the profit when 796 binoculars are produced?

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { l } 2 x + y = 8 \\2 x + 5 y = - 8\end{array} \right.$

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Exam 4: Systems of Equations and Inequalities

Solve the system of equations by the elimination method. - {−x−2y=−8−9x−18y=2\left\{ \begin{array} { r } - x - 2 y = - 8 \\- 9 x - 18 y = 2\end{array} \right.{−x−2y=−8−9x−18y=2​