Question 1

Solve the system by the substitution method.
-$$\left\{ \begin{array} { r } 
5 x - 2 y = - 1 \
x + 4 y = 35
\end{array} \right.$$

Accepted Answer

A)  $\{ ( 3,8 ) \}$ 
B)  $\{ ( 3,9 ) \}$ 
C)  $\{ ( x , y ) \mid x + 4 y = 35 \}$ 
D)  $\varnothing$ 
A)  $\{ ( 3,8 ) \}$ 
B)  $\{ ( 3,9 ) \}$ 
C)  $\{ ( x , y ) \mid x + 4 y = 35 \}$ 
D)  $\varnothing$ A

Question 2

Solve the problem.
-Given the cost function, C(x), and the revenue function, R(x), write the profit function from producing and selling x units of the product. $$\begin{array} { l } 
C ( x ) = 59 x + 1430 \
R ( x ) = 70 x
\end{array}$$

Accepted Answer

A)  $P ( x ) = - 11 x + 1430$ 
B)  $P ( x ) = - 11 x - 1430$ 
C)  $P ( x ) = 11 x - 1430$ 
D)  $P ( x ) = 11 x + 1430$ 
A)  $P ( x ) = - 11 x + 1430$ 
B)  $P ( x ) = - 11 x - 1430$ 
C)  $P ( x ) = 11 x - 1430$ 
D)  $P ( x ) = 11 x + 1430$ C

Question 3

Solve the system by graphing.
-$$\left\{ \begin{array} { l } 
3 x + y = 13 \
3 x + y = 28
\end{array} \right.$$

Accepted Answer

A)  {(9, 4)} 
B)  Ø 
C)  {(x, y) 3x + y = 13} 
D)  {(6, 10)} 
A)  {(9, 4)} 
B)  Ø 
C)  {(x, y) 3x + y = 13} 
D)  {(6, 10)} B

Question 4

Solve the problem.
-Devon purchased tickets to an air show for 8 adults and 2 children. The total cost was $170. The cost of a child's ticket was $5 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket.

Accepted Answer

A)  adult's ticket: $18; child's ticket: $13 
B)  adult's ticket: $20; child's ticket: $15 
C)  adult's ticket: $17; child's ticket: $12 
D)  adult's ticket: $19; child's ticket: $14 
A)  adult's ticket: $18; child's ticket: $13 
B)  adult's ticket: $20; child's ticket: $15 
C)  adult's ticket: $17; child's ticket: $12 
D)  adult's ticket: $19; child's ticket: $14

Question 5

Solve the problem.
-Given the cost function, C(x), and the revenue function, R(x), write the profit function from producing and selling x units of the product. $$\begin{array} { l } 
C ( x ) = 0.4 x + 450 \
R ( x ) = 0.9 x
\end{array}$$

Accepted Answer

A)  $P ( x ) = 0.5 x - 450$ 
B)  $P ( x ) = 0.5 x + 450$ 
C)  $P ( x ) = - 0.5 x - 450$ 
D)  $P ( x ) = - 0.5 x + 450$ 
A)  $P ( x ) = 0.5 x - 450$ 
B)  $P ( x ) = 0.5 x + 450$ 
C)  $P ( x ) = - 0.5 x - 450$ 
D)  $P ( x ) = - 0.5 x + 450$

Question 6

Solve the problem.
-A chemist needs 150 milliliters of a 45% solution but has only 25% and 55% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Accepted Answer

A)  100 milliliters of 25%; 50 milliliters of 55% 
B)  60 milliliters of 25%; 100 milliliters of 55% 
C)  50 milliliters of 25%; 100 milliliters of 55% 
D)  60 milliliters of 25%; 110 milliliters of 55% 
A)  100 milliliters of 25%; 50 milliliters of 55% 
B)  60 milliliters of 25%; 100 milliliters of 55% 
C)  50 milliliters of 25%; 100 milliliters of 55% 
D)  60 milliliters of 25%; 110 milliliters of 55%

Question 7

Determine if the given ordered triple is a solution of the system.
-$$\left\{ \begin{array} { r } 
( - 5,2 , - 1 ) \
x + 5 y + 5 z = 0 \
3 y + 5 z = 1 \
z = - 1
\end{array} \right.$$

Accepted Answer

A)  not a solution 
B)  solution 
A)  not a solution 
B)  solution

Question 8

Solve the problem.
-Given the cost function, $C ( x )$, and the revenue function, $R ( x )$, find the number of units $x$ that must be sold to brea
$$\begin{array} { l } 
C ( x ) = 56 x + 900 \
R ( x ) = 71 x
\end{array}$$

Accepted Answer

A)  62 units 
B)  60 units 
C)  61 units 
D)  11 units en. 
A)  62 units 
B)  60 units 
C)  61 units 
D)  11 units en.

Question 9

Solve the system by the addition method.
-$$\left\{ \begin{array} { r } 
5 x + 6 y = - 7 \
- 5 x - 13 y = 21
\end{array} \right.$$

Accepted Answer

A)  $\{ ( - 1,2 ) \}$ 
B)  $\{ ( x , y ) \mid 5 x + 6 y = - 7 \}$ 
C)  $\varnothing$ 
D)  $\{ ( 1 , - 2 ) \}$ 
A)  $\{ ( - 1,2 ) \}$ 
B)  $\{ ( x , y ) \mid 5 x + 6 y = - 7 \}$ 
C)  $\varnothing$ 
D)  $\{ ( 1 , - 2 ) \}$

Question 10

Solve the problem.
-A retired couple has $170,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 5%. The rest they want to invest in AA bonds yielding 11% per year. How much should they invest in each to realize exactly $15,700 per year?

Accepted Answer

A)  $120,000 at 11% and $50,000 at 5% 
B)  $110,000 at 5% and $60,000 at 11% 
C)  $120,000 at 5% and $50,000 at 11% 
D)  $130,000 at 11% and $40,000 at 5% 
A)  $120,000 at 11% and $50,000 at 5% 
B)  $110,000 at 5% and $60,000 at 11% 
C)  $120,000 at 5% and $50,000 at 11% 
D)  $130,000 at 11% and $40,000 at 5%

Question 11

Solve the system by any method.
-$$\left\{ \begin{array} { l } 
\frac { x } { 2 } + \frac { y } { 3 } = 4 \
\frac { x } { 4 } + \frac { y } { 6 } = 2
\end{array} \right.$$

Accepted Answer

A)  one ordered-pair solution 
B)  infinitely many solutions 
C)  no solution 
A)  one ordered-pair solution 
B)  infinitely many solutions 
C)  no solution

Question 12

Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$\left\{\begin{array}{l}
4 x+2 y+z=3 \
4 x-5 y-z=-31 \
4 x+y+3 z=3
\end{array}\right.$

Accepted Answer

A)  $\{ ( - 2,4,3 ) \}$ 
B)  $\{ ( - 2,3,4 ) \}$ 
C)  infinitely many solutions; dependent equations 
D)  no solution or $\varnothing$ 
A)  $\{ ( - 2,4,3 ) \}$ 
B)  $\{ ( - 2,3,4 ) \}$ 
C)  infinitely many solutions; dependent equations 
D)  no solution or $\varnothing$

Question 13

Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$$\left\{ \begin{array} { r r } 
x - y + 3 z & = - 1 \
4 x + z & = 0 \
x + 5 y + z & = 5
\end{array} \right.$$

Accepted Answer

A)  infinitely many solutions; dependent equations 
B)  no solution or $\emptyset \varnothing$ 
C)  $\{ ( 0,1,0 ) \}$ 
D)  $\{ ( 0,0,1 ) \}$ 
A)  infinitely many solutions; dependent equations 
B)  no solution or $\emptyset \varnothing$ 
C)  $\{ ( 0,1,0 ) \}$ 
D)  $\{ ( 0,0,1 ) \}$

Question 14

Solve the system by graphing.
-

Accepted Answer

A)  {(0, 14)} 
B)  Ø 
C)  {(5, -6)} 
D)  {(x, y) 4x + y = 14} 
A)  {(0, 14)} 
B)  Ø 
C)  {(5, -6)} 
D)  {(x, y) 4x + y = 14}

Question 15

Solve the problem.
-A basketball player scored 21 points in a game. The number of three-point field goals the player made was 29 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 7 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)  10 free throws; 5 two-point field goals; 3 three-point field goals 
B)  10 free throws; 4 two-point field goals; 1 three-point field goals 
C)  11 free throws; 4 two-point field goals; 4 three-point field goals 
D)  10 free throws; 1 two-point field goals; 4 three-point field goals 
A)  10 free throws; 5 two-point field goals; 3 three-point field goals 
B)  10 free throws; 4 two-point field goals; 1 three-point field goals 
C)  11 free throws; 4 two-point field goals; 4 three-point field goals 
D)  10 free throws; 1 two-point field goals; 4 three-point field goals

Question 16

Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$$\left\{ \begin{array} { l } 
x + y + z = 5 \
x - y + 5 z = 3 \
4 x + y + z = - 1
\end{array} \right.$$

Accepted Answer

A)  infinitely many solutions; dependent equations 
B)  $\{ ( - 2,5,2 ) \}$ 
C)  no solution or $\varnothing$ 
D)  $\{ ( 2,5 , - 2 ) \}$ 
A)  infinitely many solutions; dependent equations 
B)  $\{ ( - 2,5,2 ) \}$ 
C)  no solution or $\varnothing$ 
D)  $\{ ( 2,5 , - 2 ) \}$

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

Question 18

Determine if the given ordered triple is a solution of the system.
-$$\left\{ \begin{array} { r } 
( 1,2 , - 5 ) \
x + 4 y + 3 z = 6 \
4 y + 3 z = 11 \
z = 1
\end{array} \right.$$

Accepted Answer

A)  solution 
B)  not a solution 
A)  solution 
B)  not a solution

Question 19

Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$$\left\{ \begin{array} { r r } 
3 x - 3 y + 6 z = & - 30 \
- 15 x + 15 y - 30 z = & 150 \
12 x - 12 y + 24 z = & - 120
\end{array} \right.$$

Accepted Answer

A)  $\{ ( 4 , - 9 , - 4 ) \}$ 
B)  $\{ ( 4 , - 4 , - 9 ) \}$ 
C)  infinitely many solutions; dependent equations 
D)  no solution or $\varnothing$ 
A)  $\{ ( 4 , - 9 , - 4 ) \}$ 
B)  $\{ ( 4 , - 4 , - 9 ) \}$ 
C)  infinitely many solutions; dependent equations 
D)  no solution or $\varnothing$

Question 20

Solve the problem.
-A couple have bought a new house and are comparing quotes from two moving companies for moving their furniture. Company A charges $120 for the truck and $55 per hour for the movers. Company B charges $110 for the truck and $70 per hour for the movers. Create a cost equation for each company where y is the total cost and x is the number of hours of labor. Write a system of equations.

Accepted Answer

A)  55y = 120x 
B)  55y = x + 120 
C)  y = 55x + 120 
D)  y = 120x + 55 70y = 110x 70y = x + 110 y = 70x + 110 y = 110x + 70 
A)  55y = 120x 
B)  55y = x + 120 
C)  y = 55x + 120 
D)  y = 120x + 55 70y = 110x 70y = x + 110 y = 70x + 110 y = 110x + 70

Solve the system by the substitution method. - $\left\{ \begin{array} { r } 5 x - 2 y = - 1 \\x + 4 y = 35\end{array} \right.$

Solve the problem. -Given the cost function, C(x), and the revenue function, R(x), write the profit function from producing and selling x units of the product. C(x)=59x+1430 R(x)=70x

Solve the system by graphing. - $\left\{ \begin{array} { l } 3 x + y = 13 \\3 x + y = 28\end{array} \right.$ $Solve the system by graphing. - \left\{ \begin{array} { l } 3 x + y = 13 \\ 3 x + y = 28 \end{array} \right.$

Solve the problem. -Devon purchased tickets to an air show for 8 adults and 2 children. The total cost was $170. The cost of a child's ticket was $5 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket.

Solve the problem. -Given the cost function, C(x), and the revenue function, R(x), write the profit function from producing and selling x units of the product. C(x)=0.4x+450 R(x)=0.9x

Solve the problem. -A chemist needs 150 milliliters of a 45% solution but has only 25% and 55% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { r } ( - 5,2 , - 1 ) \\x + 5 y + 5 z = 0 \\3 y + 5 z = 1 \\z = - 1\end{array} \right.$

Solve the problem. -Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the number of units $x$ that must be sold to brea C(x)=56x+900 R(x)=71x

Solve the system by the addition method. - $\left\{ \begin{array} { r } 5 x + 6 y = - 7 \\- 5 x - 13 y = 21\end{array} \right.$

Solve the problem. -A retired couple has $170,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 5%. The rest they want to invest in AA bonds yielding 11% per year. How much should they invest in each to realize exactly $15,700 per year?

Solve the system by any method. - $\left\{ \begin{array} { l } \frac { x } { 2 } + \frac { y } { 3 } = 4 \\\frac { x } { 4 } + \frac { y } { 6 } = 2\end{array} \right.$

Solve the system. If there is no solution or if the system's equations are dependent, so state. - $\left\{\begin{array}{l}4 x+2 y+z=3 \\4 x-5 y-z=-31 \\4 x+y+3 z=3\end{array}\right.$

Solve the system. If there is no solution or if the system's equations are dependent, so state. - $\left\{ \begin{array} { r r } x - y + 3 z & = - 1 \\4 x + z & = 0 \\x + 5 y + z & = 5\end{array} \right.$

Solve the system by graphing. -

Solve the system. If there is no solution or if the system's equations are dependent, so state. - $\left\{ \begin{array} { l } x + y + z = 5 \\x - y + 5 z = 3 \\4 x + y + z = - 1\end{array} \right.$

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?

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { r } ( 1,2 , - 5 ) \\x + 4 y + 3 z = 6 \\4 y + 3 z = 11 \\z = 1\end{array} \right.$

Solve the system. If there is no solution or if the system's equations are dependent, so state. - $\left\{ \begin{array} { r r } 3 x - 3 y + 6 z = & - 30 \\- 15 x + 15 y - 30 z = & 150 \\12 x - 12 y + 24 z = & - 120\end{array} \right.$

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Exam 3: Systems of Linear Equations

Solve the system by the substitution method. - {5x−2y=−1x+4y=35\left\{ \begin{array} { r } 5 x - 2 y = - 1 \\x + 4 y = 35\end{array} \right.{5x−2y=−1x+4y=35​