Question 1

Solve the system.
-$\left\{ \begin{array} { r } 
x + y + z = - 10 \
x - y + 4 z = - 13 \
4 x + 4 y + 4 z = - 22
\end{array} \right.$

Accepted Answer

A)  $( - 4 , - 3 , - 3 )$ 
B)  $( - 3 , - 4 , - 3 )$ 
C)  $( - 3 , - 3 , - 4 )$ 
D)  $\varnothing$ 
A)  $( - 4 , - 3 , - 3 )$ 
B)  $( - 3 , - 4 , - 3 )$ 
C)  $( - 3 , - 3 , - 4 )$ 
D)  $\varnothing$

Question 2

Solve.
-A certain aircraft can fly 912 miles with the wind in 4 hours and travel the same distance against the wind in 6 hours. What is the speed of the wind?

Accepted Answer

A)  $57 \mathrm { mph }$ 
B)  $19 \mathrm { mph }$ 
C)  $38 \mathrm { mph }$ 
D)  $76 \mathrm { mph }$ 
A)  $57 \mathrm { mph }$ 
B)  $19 \mathrm { mph }$ 
C)  $38 \mathrm { mph }$ 
D)  $76 \mathrm { mph }$

Question 3

Solve the system by the substitution method or the addition method.
-$\left\{ \begin{array} { l } 
\frac { x - 2 } { 2 } = \frac { 2 - y } { 4 } \
\frac { 5 - 2 x } { 3 } = \frac { y } { 2 }
\end{array} \right.$

Accepted Answer

A)  $( 2 , - 4 )$ 
B)  $( 2,2 )$ 
C)  $( - 4,10 )$ 
D)  $( 4 , - 2 )$ 
A)  $( 2 , - 4 )$ 
B)  $( 2,2 )$ 
C)  $( - 4,10 )$ 
D)  $( 4 , - 2 )$

Question 4

Solve.
-Dmitri needs 6 liters of a $16 \%$ 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 $12 \%$ solution and the other an unlimited supply of the $24 \%$ solution. How many liters of each solution should Dmitri use?

Accepted Answer

A)  $12 \%$ solution: $4.5$ liters; $24 \%$ solution: $1.5$ liters 
B)  $12 \%$ solution: 2 liters; $24 \%$ solution: 4 liters 
C)  $12 \%$ solution: 4 liters; $24 \%$ solution: 2 liters 
D)  $12 \%$ solution: $3.5$ liters; $24 \%$ solution: $2.5$ liters 
A)  $12 \%$ solution: $4.5$ liters; $24 \%$ solution: $1.5$ liters 
B)  $12 \%$ solution: 2 liters; $24 \%$ solution: 4 liters 
C)  $12 \%$ solution: 4 liters; $24 \%$ solution: 2 liters 
D)  $12 \%$ solution: $3.5$ liters; $24 \%$ solution: $2.5$ liters

Question 5

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
4 y = x + 32 \
3 x + 12 y = 0
\end{array} \right.$

Accepted Answer

A)  $( 4 , - 16 )$ 
B)  $( - 16,4 )$ 
C)  no solution 
D)  infinite number of solutions 
A)  $( 4 , - 16 )$ 
B)  $( - 16,4 )$ 
C)  no solution 
D)  infinite number of solutions

Question 6

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.
-$\begin{array} { l } 
C ( x ) = 121 x + 234,000 \
R ( x ) = 316 x
\end{array}$

Accepted Answer

A)  458 units 
B)  1202 units 
C)  1200 units 
D)  1201 units 
A)  458 units 
B)  1202 units 
C)  1200 units 
D)  1201 units

Question 7

Solve the system of equations by the addition method.
-$\left\{ \begin{array} { l } 
0.01 x - 0.08 y = - 0.19 \
0.2 x + 0.6 y = 0.6
\end{array} \right.$

Accepted Answer

A)  infinite number of solutions 
B)  $( 0.08 , - 0.01 )$ 
C)  $( - 3,2 )$ 
D)  $( 10 , - 1.19 )$ 
A)  infinite number of solutions 
B)  $( 0.08 , - 0.01 )$ 
C)  $( - 3,2 )$ 
D)  $( 10 , - 1.19 )$

Question 8

Write a system of equations in x and y describing the situation. Do not solve the system.
-An order of 2 orders of fries, 3 hamburgers, and 3 drinks costs $\$ 11$. An order of 4 orders of fries, 2 hamburgers, and 5 drinks costs $\$ 13$. All drinks are $\$ 1$.

Accepted Answer

A)  $\left\{ \begin{array} { l } 2 x + 3 y + 3 = 11 \ 4 x + 2 y + 5 = 13 \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } ( 2 x ) ( 3 y ) + 3 = 11 \ ( 4 x ) ( 2 y ) + 5 = 13 \end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 2 x + 3 y + 1 = 11 \ 4 x + 2 y + 1 = 13 \end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 2 x + 3 y + 3 = 8 \ 4 x + 2 y + 5 = 8 \end{array} \right.$ 
A)  $\left\{ \begin{array} { l } 2 x + 3 y + 3 = 11 \ 4 x + 2 y + 5 = 13 \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } ( 2 x ) ( 3 y ) + 3 = 11 \ ( 4 x ) ( 2 y ) + 5 = 13 \end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 2 x + 3 y + 1 = 11 \ 4 x + 2 y + 1 = 13 \end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 2 x + 3 y + 3 = 8 \ 4 x + 2 y + 5 = 8 \end{array} \right.$

Question 9

Solve.
-Three trains - one eastbound, one westbound, and one northbound - leave a city at the same time. The speed of the northbound train is 40 miles per hour greater than the speed of the eastbound
Train. After 5 hours, the distance between the westbound train and the eastbound train is 450 miles.
Twice the speed of the westbound train is 50 miles per hour more than the speed of the northbound
Train. Find the speeds of the three trains.

Accepted Answer

A)  eastbound, 40 mph; westbound, 60 mph; northbound, 80 mph 
B)  eastbound, 30 mph; westbound, 60 mph; northbound, 70 mph 
C)  eastbound, 20 mph; westbound, 70 mph; northbound, 70 mph 
D)  eastbound, 70 mph; westbound, 60 mph; northbound, 30 mph 
A)  eastbound, 40 mph; westbound, 60 mph; northbound, 80 mph 
B)  eastbound, 30 mph; westbound, 60 mph; northbound, 70 mph 
C)  eastbound, 20 mph; westbound, 70 mph; northbound, 70 mph 
D)  eastbound, 70 mph; westbound, 60 mph; northbound, 30 mph

Question 10

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
- 3 y + 4 y = - 7 x + 2 ( x + 1 ) + 7 x - 1 \
5 ( x + y ) - x + y = 22
\end{array} \right.$

Accepted Answer

A)  infinite number of solutions 
B)  no solution 
C)  $( 3,1 )$ 
D)  $( 1,3 )$ 
A)  infinite number of solutions 
B)  no solution 
C)  $( 3,1 )$ 
D)  $( 1,3 )$

Question 11

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?
-$\left\{ \begin{array} { r } 
x = - y \
y + x = - 5
\end{array} \right.$

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 12

Determine whether the ordered pair is a solution of the system of linear equations.
-$(4,-1)$
$\left\{\begin{array}{l}
x+y=3 \
x-y=5
\end{array}\right.$

Accepted Answer

A) True 
 B)False

Question 13

Solve.
-Khang and Hector live $40.8$ miles apart in southeastern Missouri. They decide to bicycle towards each other and meet somewhere in between. Hector's rate of speed is $70 \%$ of Khang's. They start out at the same time and meet 4 hours later. Find Hector's rate of speed.

Accepted Answer

A)  $24 \mathrm { mph }$ 
B)  $6 \mathrm { mph }$ 
C)  $4.2 \mathrm { mph }$ 
D)  $40.8 \mathrm { mph }$ 
A)  $24 \mathrm { mph }$ 
B)  $6 \mathrm { mph }$ 
C)  $4.2 \mathrm { mph }$ 
D)  $40.8 \mathrm { mph }$

Question 14

Solve the system of equations by either the addition method or the substitution method.
-$\left\{ \begin{array} { l } 
2 x + 3 y = 18 \
3 x - 4 y = - 42.7
\end{array} \right.$

Accepted Answer

A)  $( - 3.3,8.2 )$ 
B)  no solution 
C)  infinite number of solutions 
D)  $( 8.2 , - 3.3 )$ 
A)  $( - 3.3,8.2 )$ 
B)  no solution 
C)  infinite number of solutions 
D)  $( 8.2 , - 3.3 )$

Question 15

Solve.
-A basketball player scored 34 points in a game. The number of three-point field goals the player made was 4 less than three times the number of free throws (each worth 1 point). Twice the
Number of two-point field goals the player made was 11 more than the number of three-point field
Goals made. Find the number of free-throws, two-point field goals, and three-point field goals that
The player made in the game.

Accepted Answer

A)  3 free throws; 8 two-point field goals; 5 three-point field goals 
B)  3 free throws; 5 two-point field goals; 8 three-point field goals 
C)  4 free throws; 8 two-point field goals; 8 three-point field goals 
D)  3 free throws; 9 two-point field goals; 7 three-point field goals 
A)  3 free throws; 8 two-point field goals; 5 three-point field goals 
B)  3 free throws; 5 two-point field goals; 8 three-point field goals 
C)  4 free throws; 8 two-point field goals; 8 three-point field goals 
D)  3 free throws; 9 two-point field goals; 7 three-point field goals

Question 16

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.
-$\begin{array} { l } 
C ( x ) = 15 x + 22,400 \
R ( x ) = 29 x
\end{array}$

Accepted Answer

A)  1600 units 
B)  1602 units 
C)  1601 units 
D)  521 units 
A)  1600 units 
B)  1602 units 
C)  1601 units 
D)  521 units

Question 17

Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions.
-Trish has two containers of water for a camping trip. One container holds 2 times as much as the other. The total amount of water is 21 gallons. How much water is in each container?

Accepted Answer

A)  21 gallons; 7 gallons 
B)  $7.5$ gallons; $13.5$ gallons 
C)  7 gallons; 14 gallons 
D)  6 gallons; 15 gallons 
A)  21 gallons; 7 gallons 
B)  $7.5$ gallons; $13.5$ gallons 
C)  7 gallons; 14 gallons 
D)  6 gallons; 15 gallons

Question 18

Solve the system by graphing.
-$\left\{ \begin{array} { l } x - y = - 2 \ 3 x - y = - 10 \end{array} \right.$

Accepted Answer

A)  $( - 2,4 )$ 
B)  $( 0 , - 2 )$ 
C)  $( - 4 , - 2 )$ 
D)  $( - 5 , - 1 )$ 
A)  $( - 2,4 )$ 
B)  $( 0 , - 2 )$ 
C)  $( - 4 , - 2 )$ 
D)  $( - 5 , - 1 )$

Question 19

Solve the system of equations by the addition method.
-$\left\{ \begin{array} { l } 
x + 5 y = - 25 \
3 x + 5 y = - 15
\end{array} \right.$

Accepted Answer

A)  $( 6,5 )$ 
B)  $( 5 , - 6 )$ 
C)  infinite number of solutions 
D)  no solution 
A)  $( 6,5 )$ 
B)  $( 5 , - 6 )$ 
C)  infinite number of solutions 
D)  no solution

Question 20

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

Accepted Answer

A)  (3, 6) 
B)  (-3, -6) 
C)  (-6, -3) 
D)  no solution 
A)  (3, 6) 
B)  (-3, -6) 
C)  (-6, -3) 
D)  no solution

Solve the system. - $\left\{ \begin{array} { r } x + y + z = - 10 \\x - y + 4 z = - 13 \\4 x + 4 y + 4 z = - 22\end{array} \right.$

Solve. -A certain aircraft can fly 912 miles with the wind in 4 hours and travel the same distance against the wind in 6 hours. What is the speed of the wind?

Solve the system by the substitution method or the addition method. - $\left\{ \begin{array} { l } \frac { x - 2 } { 2 } = \frac { 2 - y } { 4 } \\\frac { 5 - 2 x } { 3 } = \frac { y } { 2 }\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } 4 y = x + 32 \\3 x + 12 y = 0\end{array} \right.$

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)=121x+234,000 R(x)=316x

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 0.01 x - 0.08 y = - 0.19 \\0.2 x + 0.6 y = 0.6\end{array} \right.$

Write a system of equations in x and y describing the situation. Do not solve the system. -An order of 2 orders of fries, 3 hamburgers, and 3 drinks costs $\$ 11$ . An order of 4 orders of fries, 2 hamburgers, and 5 drinks costs $\$ 13$ . All drinks are $\$ 1$ .

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } - 3 y + 4 y = - 7 x + 2 ( x + 1 ) + 7 x - 1 \\5 ( x + y ) - x + y = 22\end{array} \right.$

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? - $\left\{ \begin{array} { r } x = - y \\y + x = - 5\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations. - $(4,-1)$ $\left\{\begin{array}{l}x+y=3 \\x-y=5\end{array}\right.$

Solve. -Khang and Hector live $40.8$ miles apart in southeastern Missouri. They decide to bicycle towards each other and meet somewhere in between. Hector's rate of speed is $70 \%$ of Khang's. They start out at the same time and meet 4 hours later. Find Hector's rate of speed.

Solve the system of equations by either the addition method or the substitution method. - $\left\{ \begin{array} { l } 2 x + 3 y = 18 \\3 x - 4 y = - 42.7\end{array} \right.$

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)=15x+22,400 R(x)=29x

Solve the system by graphing. - $\left\{ \begin{array} { l } x - y = - 2 \\ 3 x - y = - 10 \end{array} \right.$ $Solve the system by graphing. - \left\{ \begin{array} { l } x - y = - 2 \\ 3 x - y = - 10 \end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + 5 y = - 25 \\3 x + 5 y = - 15\end{array} \right.$

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

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. - {x+y+z=−10x−y+4z=−134x+4y+4z=−22\left\{ \begin{array} { r } x + y + z = - 10 \\x - y + 4 z = - 13 \\4 x + 4 y + 4 z = - 22\end{array} \right.⎩⎨⎧​x+y+z=−10x−y+4z=−134x+4y+4z=−22​