Question 1

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
- 3 x - 12 y = 9 \
2 x + 8 y = 0
\end{array} \right.$

Accepted Answer

A)  $( 0,9 )$ 
B)  infinite number of solutions 
C)  $( 9,0 )$ 
D)  no solution 
A)  $( 0,9 )$ 
B)  infinite number of solutions 
C)  $( 9,0 )$ 
D)  no solution

Question 2

Solve the system.
-$\left\{ \begin{array} { l } 
x - y + z = - 3 \
x + y + z = 7 \
x + y - z = - 1
\end{array} \right.$

Accepted Answer

A)  $( - 2,5,4 )$ 
B)  $( 4 , - 2,5 )$ 
C)  $( - 2,4,5 )$ 
D)  $\varnothing$ 
A)  $( - 2,5,4 )$ 
B)  $( 4 , - 2,5 )$ 
C)  $( - 2,4,5 )$ 
D)  $\varnothing$

Question 3

Solve the system of equations by the addition method.
-$\left\{ \begin{array} { l } 
9 x - 2 y = - 1 \
9 x - 2 y = 4
\end{array} \right.$

Accepted Answer

A)  $( - 1,4 )$ 
B)  $( 9,2 )$ 
C)  no solution 
D)  $\left( - \frac { 1 } { 2 } , \frac { 4 } { 9 } \right)$ 
A)  $( - 1,4 )$ 
B)  $( 9,2 )$ 
C)  no solution 
D)  $\left( - \frac { 1 } { 2 } , \frac { 4 } { 9 } \right)$

Question 4

Solve.
-A chemist needs 120 milliliters of a $78 \%$ solution but has only $57 \%$ and $93 \%$ solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Accepted Answer

A)  $70 \mathrm { ml }$ of $57 \% ; 50 \mathrm { ml }$ of $93 \%$ 
B)  $55 \mathrm { ml }$ of $57 \% ; 65 \mathrm { ml }$ of $93 \%$ 
C)  $55 \mathrm { ml }$ of $57 \% ; 70 \mathrm { ml }$ of $93 \%$ 
D)  $50 \mathrm { ml }$ of $57 \% ; 70 \mathrm { ml }$ of $93 \%$ 
A)  $70 \mathrm { ml }$ of $57 \% ; 50 \mathrm { ml }$ of $93 \%$ 
B)  $55 \mathrm { ml }$ of $57 \% ; 65 \mathrm { ml }$ of $93 \%$ 
C)  $55 \mathrm { ml }$ of $57 \% ; 70 \mathrm { ml }$ of $93 \%$ 
D)  $50 \mathrm { ml }$ of $57 \% ; 70 \mathrm { ml }$ of $93 \%$

Question 5

Determine whether the ordered pair is a solution of the system of linear equations.
-$(4,1)$
$\left\{ \begin{array} { l }

2 x = 9 - y \
3 x = 14 - 2 y
\end{array} \right.$

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

A)  $( - 4,2 )$ 
B)  infinite number of solutions 
C)  no solution 
D)  $( 2 , - 4 )$ 
A)  $( - 4,2 )$ 
B)  infinite number of solutions 
C)  no solution 
D)  $( 2 , - 4 )$

Question 7

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l l } 
\text { system of linear equations } & \text { solution } & \text { consistent } & \text { independent } \
\text { dependent } & \text { inconsistent } & \text { substitution } & \text { addition }
\end{array}$$
-A system of linear equations that has at least one solution is called a(n) system.

Accepted Answer

A)  inconsistent 
B)  dependent 
C)  independent 
D)  consistent 
A)  inconsistent 
B)  dependent 
C)  independent 
D)  consistent

Question 8

Determine whether the ordered pair is a solution of the system of linear equations.
-$(5,-2)$
$\left\{ \begin{array} { l } 
 
3 x + y = 17 \
4 x + 3 y = 26
\end{array} \right.$

Accepted Answer

A) True 
 B)False

Question 9

Solve.
-University Theater sold 513 tickets for a play. Tickets cost $\$ 24$ per adult and $\$ 14$ per senior citizen. If total receipts were $\$ 8482$, how many senior citizen tickets were sold?

Accepted Answer

A)  293 senior citizen tickets 
B)  383 senior citizen tickets 
C)  220 senior citizen tickets 
D)  130 senior citizen tickets 
A)  293 senior citizen tickets 
B)  383 senior citizen tickets 
C)  220 senior citizen tickets 
D)  130 senior citizen tickets

Question 10

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.  
-What is the profit when 812 binoculars are produced?

Accepted Answer

A)  $1748 
B)  $4748 
C)  $3124 
D)  $124 
A)  $1748 
B)  $4748 
C)  $3124 
D)  $124

Question 11

Solve the system.
-$\left\{ \begin{aligned}
3 x - 4 y & = - 1 \
4 y + 4 z & = 32 \
x + z & = 9
\end{aligned} \right.$

Accepted Answer

A)  $( 4,5,4 )$ 
B)  $\varnothing$ 
C)  $( 5,4,4 )$ 
D)  $( - 5,4 , - 4 )$ 
A)  $( 4,5,4 )$ 
B)  $\varnothing$ 
C)  $( 5,4,4 )$ 
D)  $( - 5,4 , - 4 )$

Question 12

Solve the system of equations by the addition method.
-$\left\{ \begin{array} { l } 
5 x - 2 y = - 17 \
5 x - \frac { 1 } { 2 } y = - 23
\end{array} \right.$

Accepted Answer

A)  $( - 4 , - 5 )$ 
B)  no solution 
C)  $( 5 , - 5 )$ 
D)  $( - 5 , - 4 )$ 
A)  $( - 4 , - 5 )$ 
B)  no solution 
C)  $( 5 , - 5 )$ 
D)  $( - 5 , - 4 )$

Question 13

Solve the system.
-$\left\{ \begin{array} { r r } 
x + y & = - 3 \
- 5 x - 5 y + 5 z & = 35 \
x - z & = - 8
\end{array} \right.$

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Without graphing, decide:
(a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point?
(b) How many solutions does the system have?
-$\left\{ \begin{array} { r } 
\frac { 1 } { 6 } x - y = 1 \
x = 6
\end{array} \right.$

Accepted Answer

A)  lines intersecting at a single point; one solution 
B)  parallel lines; no solution 
C)  identical lines; infinite number of solutions 
A)  lines intersecting at a single point; one solution 
B)  parallel lines; no solution 
C)  identical lines; infinite number of solutions

Question 16

Solve the system.
-$\left\{ \begin{array} { r r } 
x - 3 y - z = & - 5 \
5 x - 15 y - 5 z = & - 25 \
- 2 x + 6 y + 2 z = & 10
\end{array} \right.$

Accepted Answer

A)  $( 5 , - 2,16 )$ 
B)  $( - 2,5 , - 12 )$ 
C)  $\{ ( x , y , z ) \mid x - 3 y - z = - 5 \}$ 
D)  $\varnothing$ 
A)  $( 5 , - 2,16 )$ 
B)  $( - 2,5 , - 12 )$ 
C)  $\{ ( x , y , z ) \mid x - 3 y - z = - 5 \}$ 
D)  $\varnothing$

Question 17

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.  
-How many binoculars must be produced and sold for the company to break even?

Accepted Answer

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

Question 18

Solve.
-Doreen and Irena plan to leave their houses at the same time, roller blade towards each other, and meet for lunch after 2 hours on the road. Doreen can maintain a speed of $3.5$ miles per hour, which is $70 \%$ of Irena's speed. If they meet exactly as planned, what is the distance between their houses?

Accepted Answer

A)  7 miles 
B)  $11.9$ miles 
C)  10 miles 
D)  17 miles 
A)  7 miles 
B)  $11.9$ miles 
C)  10 miles 
D)  17 miles

Question 19

If the two equations in a system of linear equations are added and the result is 6x = 0, the system has no solution.

Accepted Answer

A) True 
 B)False

Question 20

A system of two linear equations in two variables can have exactly two solutions.

Accepted Answer

A) True 
 B)False

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } - 3 x - 12 y = 9 \\2 x + 8 y = 0\end{array} \right.$

Solve the system. - $\left\{ \begin{array} { l } x - y + z = - 3 \\x + y + z = 7 \\x + y - z = - 1\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 9 x - 2 y = - 1 \\9 x - 2 y = 4\end{array} \right.$

Solve. -A chemist needs 120 milliliters of a $78 \%$ solution but has only $57 \%$ and $93 \%$ solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Determine whether the ordered pair is a solution of the system of linear equations. - $(4,1)$ $\left\{ \begin{array} { l } 2 x = 9 - y \\3 x = 14 - 2 y\end{array} \right.$

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

Fill in the blank with one of the words or phrases listed below. system of linear equations solution consistent independent dependent inconsistent substitution addition -A system of linear equations that has at least one solution is called a(n) system.

Determine whether the ordered pair is a solution of the system of linear equations. - $(5,-2)$ $\left\{ \begin{array} { l } 3 x + y = 17 \\4 x + 3 y = 26\end{array} \right.$

Solve. -University Theater sold 513 tickets for a play. Tickets cost $\$ 24$ per adult and $\$ 14$ per senior citizen. If total receipts were $\$ 8482$ , how many senior citizen tickets were sold?

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -What is the profit when 812 binoculars are produced?

Solve the system. - $\left\{ \begin{aligned}3 x - 4 y & = - 1 \\4 y + 4 z & = 32 \\x + z & = 9\end{aligned} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 5 x - 2 y = - 17 \\5 x - \frac { 1 } { 2 } y = - 23\end{array} \right.$

Solve the system. - $\left\{ \begin{array} { r r } x + y & = - 3 \\- 5 x - 5 y + 5 z & = 35 \\x - z & = - 8\end{array} \right.$

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

Without graphing, decide: (a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point? (b) How many solutions does the system have? - $\left\{ \begin{array} { r } \frac { 1 } { 6 } x - y = 1 \\x = 6\end{array} \right.$

Solve the system. - $\left\{ \begin{array} { r r } x - 3 y - z = & - 5 \\5 x - 15 y - 5 z = & - 25 \\- 2 x + 6 y + 2 z = & 10\end{array} \right.$

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -How many binoculars must be produced and sold for the company to break even?

If the two equations in a system of linear equations are added and the result is 6x = 0, the system has no solution.

A system of two linear equations in two variables can have exactly two solutions.

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 4: Solving Systems of Linear Equations

Solve the system of equations by the substitution method. - {−3x−12y=92x+8y=0\left\{ \begin{array} { l } - 3 x - 12 y = 9 \\2 x + 8 y = 0\end{array} \right.{−3x−12y=92x+8y=0​

Solve the system. - {x−y+z=−3x+y+z=7x+y−z=−1\left\{ \begin{array} { l } x - y + z = - 3 \\x + y + z = 7 \\x + y - z = - 1\end{array} \right.⎩⎨⎧​x−y+z=−3x+y+z=7x+y−z=−1​

Solve the system of equations by the addition method. - {9x−2y=−19x−2y=4\left\{ \begin{array} { l } 9 x - 2 y = - 1 \\9 x - 2 y = 4\end{array} \right.{9x−2y=−19x−2y=4​

Solve. -A chemist needs 120 milliliters of a 78%78 \%78% solution but has only 57%57 \%57% and 93%93 \%93% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Determine whether the ordered pair is a solution of the system of linear equations. - (4,1)(4,1)(4,1) {2x=9−y3x=14−2y\left\{ \begin{array} { l } 2 x = 9 - y \\3 x = 14 - 2 y\end{array} \right.{2x=9−y3x=14−2y​

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

Fill in the blank with one of the words or phrases listed below. system of linear equations solution consistent independent dependent inconsistent substitution addition -A system of linear equations that has at least one solution is called a(n) system.

Determine whether the ordered pair is a solution of the system of linear equations. - (5,−2)(5,-2)(5,−2) {3x+y=174x+3y=26\left\{ \begin{array} { l } 3 x + y = 17 \\4 x + 3 y = 26\end{array} \right.{3x+y=174x+3y=26​

Solve. -University Theater sold 513 tickets for a play. Tickets cost $24\$ 24$24 per adult and $14\$ 14$14 per senior citizen. If total receipts were $8482\$ 8482$8482 , how many senior citizen tickets were sold?

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -What is the profit when 812 binoculars are produced?

Solve the system. - {3x−4y=−14y+4z=32x+z=9\left\{ \begin{aligned}3 x - 4 y & = - 1 \\4 y + 4 z & = 32 \\x + z & = 9\end{aligned} \right.⎩⎨⎧​3x−4y4y+4zx+z​=−1=32=9​

Solve the system of equations by the addition method. - {5x−2y=−175x−12y=−23\left\{ \begin{array} { l } 5 x - 2 y = - 17 \\5 x - \frac { 1 } { 2 } y = - 23\end{array} \right.{5x−2y=−175x−21​y=−23​

Solve the system. - {x+y=−3−5x−5y+5z=35x−z=−8\left\{ \begin{array} { r r } x + y & = - 3 \\- 5 x - 5 y + 5 z & = 35 \\x - z & = - 8\end{array} \right.⎩⎨⎧​x+y−5x−5y+5zx−z​=−3=35=−8​

Solve the system. - {x+y+z=0x−y+2z=−22x+y+z=−4\left\{ \begin{array} { r } x + y + z = 0 \\x - y + 2 z = - 2 \\2 x + y + z = - 4\end{array} \right.⎩⎨⎧​x+y+z=0x−y+2z=−22x+y+z=−4​

Solve the system. - {x−3y−z=−55x−15y−5z=−25−2x+6y+2z=10\left\{ \begin{array} { r r } x - 3 y - z = & - 5 \\5 x - 15 y - 5 z = & - 25 \\- 2 x + 6 y + 2 z = & 10\end{array} \right.⎩⎨⎧​x−3y−z=5x−15y−5z=−2x+6y+2z=​−5−2510​

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -How many binoculars must be produced and sold for the company to break even?

If the two equations in a system of linear equations are added and the result is 6x = 0, the system has no solution.

A system of two linear equations in two variables can have exactly two solutions.

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } - 3 x - 12 y = 9 \\2 x + 8 y = 0\end{array} \right.$

Solve the system. - $\left\{ \begin{array} { l } x - y + z = - 3 \\x + y + z = 7 \\x + y - z = - 1\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 9 x - 2 y = - 1 \\9 x - 2 y = 4\end{array} \right.$

Solve. -A chemist needs 120 milliliters of a $78 \%$ solution but has only $57 \%$ and $93 \%$ solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Determine whether the ordered pair is a solution of the system of linear equations. - $(4,1)$ $\left\{ \begin{array} { l } 2 x = 9 - y \\3 x = 14 - 2 y\end{array} \right.$

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

Determine whether the ordered pair is a solution of the system of linear equations. - $(5,-2)$ $\left\{ \begin{array} { l } 3 x + y = 17 \\4 x + 3 y = 26\end{array} \right.$

Solve. -University Theater sold 513 tickets for a play. Tickets cost $\$ 24$ per adult and $\$ 14$ per senior citizen. If total receipts were $\$ 8482$ , how many senior citizen tickets were sold?

Solve the system. - $\left\{ \begin{aligned}3 x - 4 y & = - 1 \\4 y + 4 z & = 32 \\x + z & = 9\end{aligned} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 5 x - 2 y = - 17 \\5 x - \frac { 1 } { 2 } y = - 23\end{array} \right.$

Solve the system. - $\left\{ \begin{array} { r r } x + y & = - 3 \\- 5 x - 5 y + 5 z & = 35 \\x - z & = - 8\end{array} \right.$

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

Solve the system. - $\left\{ \begin{array} { r r } x - 3 y - z = & - 5 \\5 x - 15 y - 5 z = & - 25 \\- 2 x + 6 y + 2 z = & 10\end{array} \right.$