Question 1

Which ordered pairs satisfy the system of inequalities given? $$\begin{array} { l } 
x + y  - 5
\end{array}$$

Accepted Answer

A)  $( 0,0 )$ 
B)  $( 1,5 )$ 
C)  $( 2,2 )$ 
D)  $( 6,6 )$ 
E)  $( 1 , - 6 )$ 
A)  $( 0,0 )$ 
B)  $( 1,5 )$ 
C)  $( 2,2 )$ 
D)  $( 6,6 )$ 
E)  $( 1 , - 6 )$

Question 2

In the graph of y $\leq$ 0, x $\geq$ -1 what is the corner point?

Accepted Answer

A)  (0, 0) 
B)  (0, -1) 
C)  (0, 1) 
D)  (-1, 0) 
E)  (1, 0) 
A)  (0, 0) 
B)  (0, -1) 
C)  (0, 1) 
D)  (-1, 0) 
E)  (1, 0)

Question 3

Solve by substitution: $$\begin{aligned}
y & = 12 - 4 x \
4 x + y & = 14
\end{aligned}$$

Accepted Answer

A)  (3, 0) 
B)  (4, -4) 
C)  (2, 4) 
D)  Dependent 
E)  No solution 
A)  (3, 0) 
B)  (4, -4) 
C)  (2, 4) 
D)  Dependent 
E)  No solution

Question 4

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. The I.R.Rabbit Company sells carrots. It sells six times as many pounds to grocery stores as to restaurants. It has 5,300 pounds of carrots. The company sells x pounds of carrots to grocery stores and y pounds of carrots to restaurants.

Accepted Answer

A)  $x + y = 5,300 , y = 6 x$ 
B)  $x - y = 5,300 , x = 6 y$ 
C)  $y - x = 5,300 , x = 6 y$ 
D)  $x + y = 5,300 , x = 6 y$ 
E)  $x = 5,300 + y , y = 6 x$ 
A)  $x + y = 5,300 , y = 6 x$ 
B)  $x - y = 5,300 , x = 6 y$ 
C)  $y - x = 5,300 , x = 6 y$ 
D)  $x + y = 5,300 , x = 6 y$ 
E)  $x = 5,300 + y , y = 6 x$

Question 5

Shrimp is 24.3% protein (by weight), and cooked brown rice is 2.9% protein (by weight). A mixture weighing 1113 grams is made from the shrimp and brown rice. The mixture needs to contain 63 grams of protein. How many grams of shrimp are to be used? Round to the nearest gram.

Accepted Answer

A)  969 grams of shrimp 
B)  144 grams of shrimp 
C)  139 grams of shrimp 
D)  134 grams of shrimp 
A)  969 grams of shrimp 
B)  144 grams of shrimp 
C)  139 grams of shrimp 
D)  134 grams of shrimp

Question 6

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) $$\begin{array} { l } 
y = 4 x \
y = \frac { 1 } { 4 } ( 12 + 20 x )
\end{array}$$

Accepted Answer

A)  yes 
B)  no 
C)  insufficient information 
A)  yes 
B)  no 
C)  insufficient information

Question 7

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Jacques cuts a 14-decimeter submarine sandwich into two pieces. One piece (y) is 2 decimeters longer than the other (x).

Accepted Answer

A)  x + y = 14, x = y + 2 
B)  x + y = 14, x = y - 2 
C)  x - y = 14, x = y + 2 
D)  y - x = 14, y = x - 2 
E)  y - x = 14, x = y - 2 
A)  x + y = 14, x = y + 2 
B)  x + y = 14, x = y - 2 
C)  x - y = 14, x = y + 2 
D)  y - x = 14, y = x - 2 
E)  y - x = 14, x = y - 2

Question 8

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. On a weekend, two adult movie tickets and three student tickets cost $36.50. Three adult and two student tickets cost $38.50. Find the price of the adult ticket.

Accepted Answer

A)  Adult ticket is $8.50. 
B)  Adult ticket is $6.50. 
C)  Adult ticket is $7.50. 
D)  Adult ticket is $9.50. 
E)  Adult ticket is $4.50. 
A)  Adult ticket is $8.50. 
B)  Adult ticket is $6.50. 
C)  Adult ticket is $7.50. 
D)  Adult ticket is $9.50. 
E)  Adult ticket is $4.50.

Question 9

Two DVDs and three game disks cost $137.79. Four DVDs and one game disk cost $75.73. What does one of each cost?

Accepted Answer

A)  DVD = $9.09, game disk = $39.87 
B)  DVD = $11.88, game disk = $40.09 
C)  DVD = $9.15, game disk = $39.83 
D)  DVD = $8.94, game disk = $39.97 
E)  DVD = $9.00, game disk = $39.93 
A)  DVD = $9.09, game disk = $39.87 
B)  DVD = $11.88, game disk = $40.09 
C)  DVD = $9.15, game disk = $39.83 
D)  DVD = $8.94, game disk = $39.97 
E)  DVD = $9.00, game disk = $39.93

Question 10

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Restaurants buy 10-pound and 25-pound bags of carrots. They want five times as many 10-pound bags (x) as 25-pound bags (y). If the company estimates that restaurants will buy 450 pounds of carrots, how many bags of each size should be packaged?

Accepted Answer

A)  $y = 5 x , 10 x + 25 y = 450$ 
B)  $x = 5 y , 10 y - 25 x = 450$ 
C)  $x = 5 y , x + y = 450$ 
D)  $y = 5 x , x + y = 450$ 
E)  $x = 5 y , 10 x + 25 y = 450$ 
A)  $y = 5 x , 10 x + 25 y = 450$ 
B)  $x = 5 y , 10 y - 25 x = 450$ 
C)  $x = 5 y , x + y = 450$ 
D)  $y = 5 x , x + y = 450$ 
E)  $x = 5 y , 10 x + 25 y = 450$

Question 11

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. Three adult and five university student tickets for the alternative music hall cost $86.50. Five adult and eight student tickets cost $141. Find the price of an adult ticket.

Accepted Answer

A)  Adult ticket is $8.50. 
B)  Adult ticket is $12. 
C)  Adult ticket is $13. 
D)  Adult ticket is $9.50. 
E)  Adult ticket is $15. 
A)  Adult ticket is $8.50. 
B)  Adult ticket is $12. 
C)  Adult ticket is $13. 
D)  Adult ticket is $9.50. 
E)  Adult ticket is $15.

Question 12

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. Two of the top-price tickets and eight of the lowest-price tickets for a Norah Jones concert cost $2,391. Three of the top-price and four of the lowest-price tickets cost $2,946.50. Find the cost of the top-price ticket.

Accepted Answer

A)  Top-price ticket costs $731.50 
B)  Top-price ticket costs $675.50 
C)  Top-price ticket costs $835.50 
D)  Top-price ticket costs $915.50 
E)  Top-price ticket costs $875.50 
A)  Top-price ticket costs $731.50 
B)  Top-price ticket costs $675.50 
C)  Top-price ticket costs $835.50 
D)  Top-price ticket costs $915.50 
E)  Top-price ticket costs $875.50

Question 13

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. $5 x + y = 25$

Accepted Answer

A)  $y = 25 + 5 x$ 
B)  $y = 25 x + 5$ 
C)  $y = 25 - 5 x$ 
D)  $y = 25 x - 5$ 
E)  $y = 5 x - 25$ 
A)  $y = 25 + 5 x$ 
B)  $y = 25 x + 5$ 
C)  $y = 25 - 5 x$ 
D)  $y = 25 x - 5$ 
E)  $y = 5 x - 25$

Question 14

Solve by substitution: $$\begin{aligned}
y & = 3 x + 13 \
x + 5 y & = - 15
\end{aligned}$$

Accepted Answer

A)  (-5, -2) 
B)  (-4, 1) 
C)  (-6, -5) 
D)  Dependent 
E)  No solution 
A)  (-5, -2) 
B)  (-4, 1) 
C)  (-6, -5) 
D)  Dependent 
E)  No solution

Question 15

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Ed works on two projects during one month. He works 28 hours longer on one project (y) than on the other (x). He works a total of 186 hours during the month.

Accepted Answer

A)  x + y = 186, x = y + 28 
B)  x - y = 186, x = y + 28 
C)  x + y = 186, x = y - 28 
D)  y - x = 186, y = x - 28 
E)  x - y = 186, x = y - 28 
A)  x + y = 186, x = y + 28 
B)  x - y = 186, x = y + 28 
C)  x + y = 186, x = y - 28 
D)  y - x = 186, y = x - 28 
E)  x - y = 186, x = y - 28

Question 16

Solve D = rt for r.

Accepted Answer

A)  $\frac { D } { r } = t$ 
B)  D - r = t 
C)  D - t = r 
D)  Dt = r 
E)  $\frac { D } { t } = r$ 
A)  $\frac { D } { r } = t$ 
B)  D - r = t 
C)  D - t = r 
D)  Dt = r 
E)  $\frac { D } { t } = r$

Question 17

Solve by substitution: $$\begin{aligned}
y & = - 4 - 4 x \
16 x + 4 y & = - 16
\end{aligned}$$

Accepted Answer

A)  (3, -16) 
B)  (4, -20) 
C)  (2, -12) 
D)  Dependent, $y = - 4 - 4 x$ 
E)  No solution 
A)  (3, -16) 
B)  (4, -20) 
C)  (2, -12) 
D)  Dependent, $y = - 4 - 4 x$ 
E)  No solution

Question 18

Solve by the elimination method: $$\begin{array} { l } 
10 x + 39 y = 16 \
15 x + 39 y = 18
\end{array}$$

Accepted Answer

A)  $\left( \frac { 1 } { 3 } , \frac { 4 } { 13 } \right)$ 
B)  $\left( \frac { 2 } { 5 } , \frac { 4 } { 13 } \right)$ 
C)  $\left( \frac { 2 } { 5 } , \frac { 1 } { 3 } \right)$ 
D)  $\left( \frac { 1 } { 3 } , \frac { 1 } { 3 } \right)$ 
E)  No solution 
A)  $\left( \frac { 1 } { 3 } , \frac { 4 } { 13 } \right)$ 
B)  $\left( \frac { 2 } { 5 } , \frac { 4 } { 13 } \right)$ 
C)  $\left( \frac { 2 } { 5 } , \frac { 1 } { 3 } \right)$ 
D)  $\left( \frac { 1 } { 3 } , \frac { 1 } { 3 } \right)$ 
E)  No solution

Question 19

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. Two of the top-price tickets and five of the lowest-price tickets for a Tim McGraw concert cost $660. Three of the top-price and three of the lowest-price tickets cost $900. Find the cost of the top-price ticket.

Accepted Answer

A)  Top-price ticket costs $270. 
B)  Top-price ticket costs $105. 
C)  Top-price ticket costs $230. 
D)  Top-price ticket costs $280. 
E)  Top-price ticket costs $250. 
A)  Top-price ticket costs $270. 
B)  Top-price ticket costs $105. 
C)  Top-price ticket costs $230. 
D)  Top-price ticket costs $280. 
E)  Top-price ticket costs $250.

Question 20

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $$\begin{array} { l } 
y + x = 30 \
2 x = 60 - 2 y
\end{array}$$

Accepted Answer

A)  yes 
B)  no 
C)  insufficient information 
A)  yes 
B)  no 
C)  insufficient information

Which ordered pairs satisfy the system of inequalities given? x+y<5 x+y>-5

In the graph of y $\leq$ 0, x $\geq$ -1 what is the corner point?

Solve by substitution: y =12-4x 4x+y =14

Shrimp is 24.3% protein (by weight), and cooked brown rice is 2.9% protein (by weight). A mixture weighing 1113 grams is made from the shrimp and brown rice. The mixture needs to contain 63 grams of protein. How many grams of shrimp are to be used? Round to the nearest gram.

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) y=4x y=(12+20x)

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Jacques cuts a 14-decimeter submarine sandwich into two pieces. One piece (y) is 2 decimeters longer than the other (x).

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. On a weekend, two adult movie tickets and three student tickets cost $36.50. Three adult and two student tickets cost $38.50. Find the price of the adult ticket.

Two DVDs and three game disks cost $137.79. Four DVDs and one game disk cost $75.73. What does one of each cost?

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. Three adult and five university student tickets for the alternative music hall cost $86.50. Five adult and eight student tickets cost $141. Find the price of an adult ticket.

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. $5 x + y = 25$

Solve by substitution: y =3x+13 x+5y =-15

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Ed works on two projects during one month. He works 28 hours longer on one project (y) than on the other (x). He works a total of 186 hours during the month.

Solve D = rt for r.

Solve by substitution: y =-4-4x 16x+4y =-16

Solve by the elimination method: 10x+39y=16 15x+39y=18

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) y+x=30 2x=60-2y

Algebraic Representations

Operations With Real Numbers

Solving Equations

Ratios, Rates, and Proportional Reasoning

Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Polynomial Expressions

Squares and Square Roots

Rational Expressions

Filters

Exam 6: Systems of Equations

Which ordered pairs satisfy the system of inequalities given? x+y<5 x+y>-5

In the graph of y ≤\leq≤ 0, x ≥\geq≥ -1 what is the corner point?

Solve by substitution: y =12-4x 4x+y =14

Shrimp is 24.3% protein (by weight), and cooked brown rice is 2.9% protein (by weight). A mixture weighing 1113 grams is made from the shrimp and brown rice. The mixture needs to contain 63 grams of protein. How many grams of shrimp are to be used? Round to the nearest gram.

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) y=4x y=(12+20x)

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Jacques cuts a 14-decimeter submarine sandwich into two pieces. One piece (y) is 2 decimeters longer than the other (x).

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. On a weekend, two adult movie tickets and three student tickets cost $36.50. Three adult and two student tickets cost $38.50. Find the price of the adult ticket.

Two DVDs and three game disks cost $137.79. Four DVDs and one game disk cost $75.73. What does one of each cost?

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. Three adult and five university student tickets for the alternative music hall cost $86.50. Five adult and eight student tickets cost $141. Find the price of an adult ticket.

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. 5x+y=255 x + y = 255x+y=25

Solve by substitution: y =3x+13 x+5y =-15

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Ed works on two projects during one month. He works 28 hours longer on one project (y) than on the other (x). He works a total of 186 hours during the month.

Solve D = rt for r.

Solve by substitution: y =-4-4x 16x+4y =-16

Solve by the elimination method: 10x+39y=16 15x+39y=18

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) y+x=30 2x=60-2y

Algebraic Representations

Operations With Real Numbers

Solving Equations

Ratios, Rates, and Proportional Reasoning

Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Polynomial Expressions

Squares and Square Roots

Rational Expressions

Filters

In the graph of y $\leq$ 0, x $\geq$ -1 what is the corner point?

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. $5 x + y = 25$