Question 1

Solve the system.
-$$\left\{ \begin{array} { r } 
x - y + 4 z = - 1 \
2 x + z = 0 \
- x + y - 4 z = 2
\end{array} \right.$$

Accepted Answer

A)  $( 4,1,0 )$ 
B)  $( 0,1,0 )$ 
C)  $( 0,0,1 )$ 
D)  $\varnothing$ 
A)  $( 4,1,0 )$ 
B)  $( 0,1,0 )$ 
C)  $( 0,0,1 )$ 
D)  $\varnothing$

Question 2

Write the word or phrase that best completes each statement or answers the question.
The revenue equation for a certain brand of mouthwash is y = 1.3x, where x is the number of bottles of mouthwash sold
and y is the total income for selling x bottles. The cost equation is y = 0.5x + 2500, where x is the number of bottles of
mouthwash manufactured and y is the cost of producing x bottles. The following set of axes shows the graph of the cost
and revenue equations.  
-Find the coordinates of the point of intersection, or breakeven point, by solving the system and explain its meaning.
$\left\{ \begin{array} { l } 
y = 1.3 x \
y = 0.5 x + 2500
\end{array} \right.$

Accepted Answer

(3125, 4062.5)
When

Question 3

Solve the system of equations by the elimination method.
-$$\left\{ \begin{array} { l } 
8 x + 6 y = 32 \
2 x + 6 y = 62
\end{array} \right.$$

Accepted Answer

A)  $( - 5,12 )$ 
B)  $( 8 , - 12 )$ 
C)  $( 6 , - 12 )$ 
D)  $\varnothing$ 
A)  $( - 5,12 )$ 
B)  $( 8 , - 12 )$ 
C)  $( 6 , - 12 )$ 
D)  $\varnothing$

Question 4

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.
-Use the revenue and cost functions to write the profit function from producing and selling $x$ binoculars.

Accepted Answer

A)  $P ( x ) = 2 x + 1500$ 
B)  $P ( x ) = 4 x + 1500$ 
C)  $\mathrm { P } ( \mathrm { x } ) = 2 \mathrm { x } - 1500$ 
D)  $\mathrm { P } ( \mathrm { x } ) = 4 \mathrm { x } - 1500$ 
A)  $P ( x ) = 2 x + 1500$ 
B)  $P ( x ) = 4 x + 1500$ 
C)  $\mathrm { P } ( \mathrm { x } ) = 2 \mathrm { x } - 1500$ 
D)  $\mathrm { P } ( \mathrm { x } ) = 4 \mathrm { x } - 1500$

Question 5

Solve the system of linear equations using matrices.
-$$\left\{ \begin{array} { r } 
6 x - 4 y = - 4 \
18 x - 12 y = 3
\end{array} \right.$$

Accepted Answer

A)  $( - 4,3 )$ 
B)  $( 3,3 )$ 
C)  $\{ ( x , y ) \mid 6 x - 4 y = - 4 \}$ 
D)  $\varnothing$ 
A)  $( - 4,3 )$ 
B)  $( 3,3 )$ 
C)  $\{ ( x , y ) \mid 6 x - 4 y = - 4 \}$ 
D)  $\varnothing$

Question 6

Solve the system of equations by the substitution method.
-$$\left\{ \begin{array} { r r } 
x + 6 y & = 7 \
- 4 x + 7 y & = - 28
\end{array} \right.$$

Accepted Answer

A)  $( - 7 , - 1 )$ 
B)  $( 7,0 )$ 
C)  $( 8,7 )$ 
D)  $\varnothing$ 
A)  $( - 7 , - 1 )$ 
B)  $( 7,0 )$ 
C)  $( 8,7 )$ 
D)  $\varnothing$

Question 7

Solve the system of equations by graphically and then solve by the elimination method or the substitution method.
-$$\left\{ \begin{array} { r } 
x - 2 y = 7 \
3 x + 2 y = 5
\end{array} \right.$$

Accepted Answer

A)  $( - 2,3 )$ 
B)  $( 3,2 )$ 
C)  $( 3 , - 2 )$ 
D)  $\varnothing$ 
A)  $( - 2,3 )$ 
B)  $( 3,2 )$ 
C)  $( 3 , - 2 )$ 
D)  $\varnothing$

Question 8

Graph the solution of the system of linear inequalities.
-$\left\{\begin{array}{l}
2 x+5 y>15 \
x-2 y<-4
\end{array}\right.$

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Solve the system of equations by the substitution method.
-$$\left\{ \begin{array} { r } 
x - \frac { 5 } { 3 } y = - 4 \
- \frac { 7 } { 3 } x + y = \frac { 2 } { 3 }
\end{array} \right.$$

Accepted Answer

A)  $( - 1 , - 3 )$ 
B)  $( 1 , - 3 )$ 
C)  $( - 1,3 )$ 
D)  $( 1,3 )$ 
A)  $( - 1 , - 3 )$ 
B)  $( 1 , - 3 )$ 
C)  $( - 1,3 )$ 
D)  $( 1,3 )$

Question 11

Determine whether the ordered pair is a solution of the system of linear equations
$( - 1 , - 3 ) , \left\{ \begin{array} { l } 
2 \mathrm { x } = - 1 - \mathrm { y } \
3 \mathrm { x } = - 3 - 2 \mathrm { y }
\end{array} \right.$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 12

Write the word or phrase that best completes each statement or answers the question.
The revenue equation for a certain brand of mouthwash is y = 1.3x, where x is the number of bottles of mouthwash sold
and y is the total income for selling x bottles. The cost equation is y = 0.5x + 2500, where x is the number of bottles of
mouthwash manufactured and y is the cost of producing x bottles. The following set of axes shows the graph of the cost
and revenue equations.  
-$$\left\{ \begin{array} { l } 
\frac { 1 } { x } + y = 20 \
\frac { 3 } { x } + y = 32
\end{array} \right.$$

Accepted Answer

A)  $\left( \frac { 1 } { 6 } , - 14 \right)$ 
B)  $\left( 14 , \frac { 1 } { 6 } \right)$ 
C)  $\left( \frac { 1 } { 6 } , 14 \right)$ 
D)  $\left( - \frac { 1 } { 6 } , - 14 \right)$ 
A)  $\left( \frac { 1 } { 6 } , - 14 \right)$ 
B)  $\left( 14 , \frac { 1 } { 6 } \right)$ 
C)  $\left( \frac { 1 } { 6 } , 14 \right)$ 
D)  $\left( - \frac { 1 } { 6 } , - 14 \right)$

Question 13

Solve the system of linear equations using matrices.
-$$\left\{ \begin{array} { l } 
x + y = - 6 \
x - y = 2
\end{array} \right.$$

Accepted Answer

A)  $( - 2 , - 4 )$ 
B)  $( - 4 , - 2 )$ 
C)  $( - 2,4 )$ 
D)  $\varnothing$ 
A)  $( - 2 , - 4 )$ 
B)  $( - 4 , - 2 )$ 
C)  $( - 2,4 )$ 
D)  $\varnothing$

Question 14

Determine whether the ordered pair is a solution of the system of linear equations
$( - 3,5 ) , \left\{ \begin{array} { l } 
x + y = 2 \
x - y = - 8
\end{array} \right.$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 15

Solve the system of equations.
-$$\left\{ \begin{array} { l } 
3.5 x + 0.2 y = - 10.9 \
0.7 x - 0.6 y = - 0.9
\end{array} \right.$$

Accepted Answer

A)  $( 0.5 , - 1.8 )$ 
B)  $( - 3 , - 2 )$ 
C)  $( - 6.5 , - 1.8 )$ 
D)  $( - 3.2 , - 2 )$ 
A)  $( 0.5 , - 1.8 )$ 
B)  $( - 3 , - 2 )$ 
C)  $( - 6.5 , - 1.8 )$ 
D)  $( - 3.2 , - 2 )$

Question 16

Determine whether the ordered pair is a solution of the system of linear equations $( 5,3 ) , \left\{ \begin{array} { l } 
2 x = 13 - y \
3 x = 21 - 2 y
\end{array} \right.$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 17

Solve the system of linear equations using matrices.
-$$\left\{ \begin{array} { r } 
- x + y = 3 \
- 3 x + y = 7
\end{array} \right.$$

Accepted Answer

A)  $( 1 , - 2 )$ 
B)  $( 2 , - 1 )$ 
C)  $( - 2,1 )$ 
D)  $\varnothing$ 
A)  $( 1 , - 2 )$ 
B)  $( 2 , - 1 )$ 
C)  $( - 2,1 )$ 
D)  $\varnothing$

Question 18

Solve the system of equations.
-$$\left\{ \begin{aligned}
y & = \frac { 1 } { 5 } x + 6 \
x - 5 y & = - 30
\end{aligned} \right.$$

Accepted Answer

A)  $( 0,6 )$ 
B)  $( - 30,0 )$ 
C)  $\left\{ ( x , y ) \mid y = \frac { 1 } { 5 } x + 6 \right\}$ 
D)  $\varnothing$ 
A)  $( 0,6 )$ 
B)  $( - 30,0 )$ 
C)  $\left\{ ( x , y ) \mid y = \frac { 1 } { 5 } x + 6 \right\}$ 
D)  $\varnothing$

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.
-A store sells tents, sleeping bags, and camp stools. A customer buys a tent, 4 sleeping bags, and 3 camp stools for $220. The price of the tent is 7 times the cost of a camp stool. The cost of a sleeping bag is $20 more than the
Cost of a camp stool. Find the cost of each item.

Accepted Answer

A)  $77 for a tent; $30 for a sleeping bag; $11 for a camp stool 
B)  $70 for a tent; $35 for a sleeping bag; $15 for a camp stool 
C)  $70 for a tent; $30 for a sleeping bag; $10 for a camp stool 
D)  $70 for a tent; $30 for a sleeping bag; $11 for a camp stool 
A)  $77 for a tent; $30 for a sleeping bag; $11 for a camp stool 
B)  $70 for a tent; $35 for a sleeping bag; $15 for a camp stool 
C)  $70 for a tent; $30 for a sleeping bag; $10 for a camp stool 
D)  $70 for a tent; $30 for a sleeping bag; $11 for a camp stool

Question 20

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l } 
\text { matrix consistent system of equations triple } \
\text { solution inconsistent element } \
\text { column }
\end{array}$$
-A(n) is a rectangular array of numbers.

Accepted Answer

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

Solve the system. - $\left\{ \begin{array} { r } x - y + 4 z = - 1 \\2 x + z = 0 \\- x + y - 4 z = 2\end{array} \right.$

Solve the system of equations by the elimination method. - $\left\{ \begin{array} { l } 8 x + 6 y = 32 \\2 x + 6 y = 62\end{array} \right.$

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. -Use the revenue and cost functions to write the profit function from producing and selling $x$ binoculars.

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { r } 6 x - 4 y = - 4 \\18 x - 12 y = 3\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r r } x + 6 y & = 7 \\- 4 x + 7 y & = - 28\end{array} \right.$

Graph the solution of the system of linear inequalities. - $\left\{\begin{array}{l}2 x+5 y>15 \\x-2 y<-4\end{array}\right.$ $Graph the solution of the system of linear inequalities. - \left\{\begin{array}{l} 2 x+5 y>15 \\ x-2 y<-4 \end{array}\right.$

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

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x - \frac { 5 } { 3 } y = - 4 \\- \frac { 7 } { 3 } x + y = \frac { 2 } { 3 }\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( - 1 , - 3 ) , \left\{ \begin{array} { l } 2 \mathrm { x } = - 1 - \mathrm { y } \\3 \mathrm { x } = - 3 - 2 \mathrm { y }\end{array} \right.$

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { l } x + y = - 6 \\x - y = 2\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( - 3,5 ) , \left\{ \begin{array} { l } x + y = 2 \\x - y = - 8\end{array} \right.$

Solve the system of equations. - $\left\{ \begin{array} { l } 3.5 x + 0.2 y = - 10.9 \\0.7 x - 0.6 y = - 0.9\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( 5,3 ) , \left\{ \begin{array} { l } 2 x = 13 - y \\3 x = 21 - 2 y\end{array} \right.$

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { r } - x + y = 3 \\- 3 x + y = 7\end{array} \right.$

Solve the system of equations. - $\left\{ \begin{aligned}y & = \frac { 1 } { 5 } x + 6 \\x - 5 y & = - 30\end{aligned} \right.$

Fill in the blank with one of the words or phrases listed below. matrix consistent system of equations triple solution inconsistent element column -A(n) is a rectangular array of numbers.

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 4: Systems of Equations and Inequalities

Solve the system. - {x−y+4z=−12x+z=0−x+y−4z=2\left\{ \begin{array} { r } x - y + 4 z = - 1 \\2 x + z = 0 \\- x + y - 4 z = 2\end{array} \right.⎩⎨⎧​x−y+4z=−12x+z=0−x+y−4z=2​

Solve the system of equations by the elimination method. - {8x+6y=322x+6y=62\left\{ \begin{array} { l } 8 x + 6 y = 32 \\2 x + 6 y = 62\end{array} \right.{8x+6y=322x+6y=62​

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. -Use the revenue and cost functions to write the profit function from producing and selling xxx binoculars.

Solve the system of linear equations using matrices. - {6x−4y=−418x−12y=3\left\{ \begin{array} { r } 6 x - 4 y = - 4 \\18 x - 12 y = 3\end{array} \right.{6x−4y=−418x−12y=3​

Solve the system of equations by the substitution method. - {x+6y=7−4x+7y=−28\left\{ \begin{array} { r r } x + 6 y & = 7 \\- 4 x + 7 y & = - 28\end{array} \right.{x+6y−4x+7y​=7=−28​

Solve the system of equations by graphically and then solve by the elimination method or the substitution method. - {x−2y=73x+2y=5\left\{ \begin{array} { r } x - 2 y = 7 \\3 x + 2 y = 5\end{array} \right.{x−2y=73x+2y=5​

Graph the solution of the system of linear inequalities. - {2x+5y>15x−2y<−4\left\{\begin{array}{l}2 x+5 y>15 \\x-2 y<-4\end{array}\right.{2x+5y>15x−2y<−4​

Graph the solution of the system of linear inequalities. - {y≥x+2y≤4−x\left\{ \begin{array} { l } y \geq x + 2 \\y \leq 4 - x\end{array} \right.{y≥x+2y≤4−x​

Solve the system of equations by the substitution method. - {x−53y=−4−73x+y=23\left\{ \begin{array} { r } x - \frac { 5 } { 3 } y = - 4 \\- \frac { 7 } { 3 } x + y = \frac { 2 } { 3 }\end{array} \right.{x−35​y=−4−37​x+y=32​​

Solve the system of linear equations using matrices. - {x+y=−6x−y=2\left\{ \begin{array} { l } x + y = - 6 \\x - y = 2\end{array} \right.{x+y=−6x−y=2​

Determine whether the ordered pair is a solution of the system of linear equations (−3,5),{x+y=2x−y=−8( - 3,5 ) , \left\{ \begin{array} { l } x + y = 2 \\x - y = - 8\end{array} \right.(−3,5),{x+y=2x−y=−8​

Solve the system of equations. - {3.5x+0.2y=−10.90.7x−0.6y=−0.9\left\{ \begin{array} { l } 3.5 x + 0.2 y = - 10.9 \\0.7 x - 0.6 y = - 0.9\end{array} \right.{3.5x+0.2y=−10.90.7x−0.6y=−0.9​

Determine whether the ordered pair is a solution of the system of linear equations (5,3),{2x=13−y3x=21−2y( 5,3 ) , \left\{ \begin{array} { l } 2 x = 13 - y \\3 x = 21 - 2 y\end{array} \right.(5,3),{2x=13−y3x=21−2y​

Solve the system of linear equations using matrices. - {−x+y=3−3x+y=7\left\{ \begin{array} { r } - x + y = 3 \\- 3 x + y = 7\end{array} \right.{−x+y=3−3x+y=7​

Solve the system of equations. - {y=15x+6x−5y=−30\left\{ \begin{aligned}y & = \frac { 1 } { 5 } x + 6 \\x - 5 y & = - 30\end{aligned} \right.⎩⎨⎧​yx−5y​=51​x+6=−30​

Fill in the blank with one of the words or phrases listed below. matrix consistent system of equations triple solution inconsistent element column -A(n) is a rectangular array of numbers.

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Solve the system. - $\left\{ \begin{array} { r } x - y + 4 z = - 1 \\2 x + z = 0 \\- x + y - 4 z = 2\end{array} \right.$

Solve the system of equations by the elimination method. - $\left\{ \begin{array} { l } 8 x + 6 y = 32 \\2 x + 6 y = 62\end{array} \right.$

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. -Use the revenue and cost functions to write the profit function from producing and selling $x$ binoculars.

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { r } 6 x - 4 y = - 4 \\18 x - 12 y = 3\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r r } x + 6 y & = 7 \\- 4 x + 7 y & = - 28\end{array} \right.$

Graph the solution of the system of linear inequalities. - $\left\{\begin{array}{l}2 x+5 y>15 \\x-2 y<-4\end{array}\right.$ $Graph the solution of the system of linear inequalities. - \left\{\begin{array}{l} 2 x+5 y>15 \\ x-2 y<-4 \end{array}\right.$

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

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x - \frac { 5 } { 3 } y = - 4 \\- \frac { 7 } { 3 } x + y = \frac { 2 } { 3 }\end{array} \right.$

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { l } x + y = - 6 \\x - y = 2\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( - 3,5 ) , \left\{ \begin{array} { l } x + y = 2 \\x - y = - 8\end{array} \right.$

Solve the system of equations. - $\left\{ \begin{array} { l } 3.5 x + 0.2 y = - 10.9 \\0.7 x - 0.6 y = - 0.9\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( 5,3 ) , \left\{ \begin{array} { l } 2 x = 13 - y \\3 x = 21 - 2 y\end{array} \right.$

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { r } - x + y = 3 \\- 3 x + y = 7\end{array} \right.$

Solve the system of equations. - $\left\{ \begin{aligned}y & = \frac { 1 } { 5 } x + 6 \\x - 5 y & = - 30\end{aligned} \right.$