Question 1

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

Accepted Answer

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

Question 2

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. $4 x - y = 17$

Accepted Answer

A)  $y = 4 x + 17$ 
B)  $y = 17 x + 4$ 
C)  $y = 17 x - 4$ 
D)  $y = 17 - 4 x$ 
E)  $y = 4 x - 17$ 
A)  $y = 4 x + 17$ 
B)  $y = 17 x + 4$ 
C)  $y = 17 x - 4$ 
D)  $y = 17 - 4 x$ 
E)  $y = 4 x - 17$ E

Question 3

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

Accepted Answer

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

Question 4

Graph the system of inequalities and show the solution set. $$\left\{ \begin{array} { l } 
y \leq - x - 1 \
y \geq 2 x - 2
\end{array} \right.$$

Accepted Answer

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

Question 5

Identify two appropriate variables, and use the variables to write equations. Use either the elimination method or the substitution method to solve the equation The sum of two numbers is $40$ . There difference is $6$ .
Find the numbers.

Accepted Answer

A)  $23.5,16.5$ 
B)  $23,17$ 
C)  $18,12$ 
D)  $25,15$ 
E)  $26,14$ 
A)  $23.5,16.5$ 
B)  $23,17$ 
C)  $18,12$ 
D)  $25,15$ 
E)  $26,14$

Question 6

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $$\begin{array} { l } 
y = x + 0.04 x \
y = 1.04 x
\end{array}$$

Accepted Answer

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

Question 7

A parallelogram has angles A and B as supplementary angles. The measure of angle A is 74 degrees more than angle B. What is the measure of angle A?

Accepted Answer

A)  A = 53 degrees 
B)  A = 67 degrees 
C)  A = 82 degrees 
D)  A = 127 degrees 
E)  A = 113 degrees 
A)  A = 53 degrees 
B)  A = 67 degrees 
C)  A = 82 degrees 
D)  A = 127 degrees 
E)  A = 113 degrees

Question 8

Which ordered pairs satisfy the system of inequalities given? $$\begin{array} { l } 
y \leq x + 4 \
y \geq x - 4
\end{array}$$

Accepted Answer

A)  $( 1,1 )$ 
B)  $( 1 , - 4 )$ 
C)  $( - 5,5 )$ 
D)  $( - 6,6 )$ 
E)  $( 1 , - 6 )$ 
A)  $( 1,1 )$ 
B)  $( 1 , - 4 )$ 
C)  $( - 5,5 )$ 
D)  $( - 6,6 )$ 
E)  $( 1 , - 6 )$

Question 9

Which ordered pairs satisfy the system of inequalities given? $$\begin{array} { l } 
y \leq - x - 4 \
y \geq x
\end{array}$$

Accepted Answer

A)  $( 0,0 )$ 
B)  $( 0 , - 1 )$ 
C)  $( - 4,4 )$ 
D)  $( - 4 , - 4 )$ 
E)  $( - 6 , - 6 )$ 
A)  $( 0,0 )$ 
B)  $( 0 , - 1 )$ 
C)  $( - 4,4 )$ 
D)  $( - 4 , - 4 )$ 
E)  $( - 6 , - 6 )$

Question 10

Solve by substitution: $$\begin{array} { l } 
5 x - 5 y = - 5 \
4 x + 2 y = 20
\end{array}$$

Accepted Answer

A)  (13, 14) 
B)  (8, 9) 
C)  (3, 4) 
D)  Dependent 
E)  No solution 
A)  (13, 14) 
B)  (8, 9) 
C)  (3, 4) 
D)  Dependent 
E)  No solution

Question 11

Nerine combines walking (at 6 km/hr) and running (at 18 km/hr) in her fitness program. Last week she exercised a total of 10 hours and traveled 108 kilometers. How many hours did she walk?

Accepted Answer

A)  5 hours 
B)  6 hours 
C)  4 hours 
D)  8 hours 
E)  2 hours 
A)  5 hours 
B)  6 hours 
C)  4 hours 
D)  8 hours 
E)  2 hours

Question 12

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Nancy has $3.50. She has only dimes (x) and quarters (y). She has 30 coins altogether.

Accepted Answer

A)  x = 30 - y, 0.10x + 0.25y = 3.50 
B)  $x - y = 30,0.10 x + 0.25 y = 3.50$ 
C)  y - x = 30, 0.10x + 0.25y = 3.50 
D)  x + y = 30, 0.05x + 0.25y = 3.50 
E)  $x + y = 30,0.05 y + 0.25 x = 3.50$ 
A)  x = 30 - y, 0.10x + 0.25y = 3.50 
B)  $x - y = 30,0.10 x + 0.25 y = 3.50$ 
C)  y - x = 30, 0.10x + 0.25y = 3.50 
D)  x + y = 30, 0.05x + 0.25y = 3.50 
E)  $x + y = 30,0.05 y + 0.25 x = 3.50$

Question 13

Solve 10 = m(4) + b for m.

Accepted Answer

A)  $2.5 - \frac { b } { 4 } = m$ 
B)  $\frac { 10 } { 4 } - b = m$ 
C)  $10 - \frac { b } { 4 } = m$ 
D)  40 - 4b = m 
E)  2.5 - b = m 
A)  $2.5 - \frac { b } { 4 } = m$ 
B)  $\frac { 10 } { 4 } - b = m$ 
C)  $10 - \frac { b } { 4 } = m$ 
D)  40 - 4b = m 
E)  2.5 - b = m

Question 14

Solve by the elimination method: $$\begin{array} { l } 
2 x - 4 y = 6 \
5 x + 5 y = - 15
\end{array}$$

Accepted Answer

A)  (-5, -4) 
B)  (3, 0) 
C)  (-1, -2) 
D)  Dependent 
E)  No solution 
A)  (-5, -4) 
B)  (3, 0) 
C)  (-1, -2) 
D)  Dependent 
E)  No solution

Question 15

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. A boat travels 20 miles downstream in an hour. While its passengers are fishing, the tide comes in. The tidewater reaches 20 miles upstream. The trip home on still water take 1 $\frac { 1 } { 4 }$ hours. Find the speed of the current, c.

Accepted Answer

A)  c = 1.5 mph 
B)  c = 2.0 mph 
C)  c = 2.5 mph 
D)  c = 3.0 mph 
E)  c = 4.0 mph 
A)  c = 1.5 mph 
B)  c = 2.0 mph 
C)  c = 2.5 mph 
D)  c = 3.0 mph 
E)  c = 4.0 mph

Question 16

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Alexandra works for two clients during one month. She works a total of 180 hours during the month. She works 50 hours more for one client (y) than for the other (x).

Accepted Answer

A)  x + y = 180, x = y + 50 
B)  x - y = 180, x = y + 50 
C)  y - x = 180, y = x - 50 
D)  $x + y = 180 , y = x + 50$ 
E)  x + y = 180, x - y = 50 
A)  x + y = 180, x = y + 50 
B)  x - y = 180, x = y + 50 
C)  y - x = 180, y = x - 50 
D)  $x + y = 180 , y = x + 50$ 
E)  x + y = 180, x - y = 50

Question 17

In the graph of x < 1, y $\geq$ -2, what is the corner point?

Accepted Answer

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

Question 18

A right triangle has angles A and B as complementary angles. The measure of angle A is 8 more than the measure of angle B. What is the measure of angle A?

Accepted Answer

A)  A = 94 degrees 
B)  A = 86 degrees 
C)  A = 41 degrees 
D)  A = 53 degrees 
E)  A = 49 degrees 
A)  A = 94 degrees 
B)  A = 86 degrees 
C)  A = 41 degrees 
D)  A = 53 degrees 
E)  A = 49 degrees

Question 19

To cut costs, the new manager at Healthy Options wants to mix 4,000 pounds of cat food. The mixture is to have 10% protein. The first ingredient contains 8% protein. The second has 13% protein. How many pounds of the 8% protein ingredient is needed?

Accepted Answer

A)  1,200 pounds of 8% 
B)  2,400 pounds of 8% 
C)  1,360 pounds of 8% 
D)  1,880 pounds of 8% 
E)  1,500 pounds of 8% 
A)  1,200 pounds of 8% 
B)  2,400 pounds of 8% 
C)  1,360 pounds of 8% 
D)  1,880 pounds of 8% 
E)  1,500 pounds of 8%

Question 20

Graph the system of Inequalities and show the solution set. Label the corner point. $$\begin{array} { l } 
y > 5 x - 5 \
y < 2 x - 2
\end{array}$$

Accepted Answer

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

In the graph of y $\geq$ 1, x $\leq$ 0 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. $4 x - y = 17$

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) 2x+y=4 2y+x=4

Graph the system of inequalities and show the solution set. $\left\{ \begin{array} { l } y \leq - x - 1 \\y \geq 2 x - 2\end{array} \right.$

Identify two appropriate variables, and use the variables to write equations. Use either the elimination method or the substitution method to solve the equation The sum of two numbers is $40$ _.There difference is $6$ . Find the numbers.

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) y=x+0.04x y=1.04x

A parallelogram has angles A and B as supplementary angles. The measure of angle A is 74 degrees more than angle B. What is the measure of angle A?

Which ordered pairs satisfy the system of inequalities given? y\leqx+4 y\geqx-4

Which ordered pairs satisfy the system of inequalities given? y\leq-x-4 y\geqx

Solve by substitution: 5x-5y=-5 4x+2y=20

Nerine combines walking (at 6 km/hr) and running (at 18 km/hr) in her fitness program. Last week she exercised a total of 10 hours and traveled 108 kilometers. How many hours did she walk?

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Nancy has $3.50. She has only dimes (x) and quarters (y). She has 30 coins altogether.

Solve 10 = m(4) + b for m.

Solve by the elimination method: 2x-4y=6 5x+5y=-15

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Alexandra works for two clients during one month. She works a total of 180 hours during the month. She works 50 hours more for one client (y) than for the other (x).

In the graph of x < 1, y $\geq$ -2, what is the corner point?

A right triangle has angles A and B as complementary angles. The measure of angle A is 8 more than the measure of angle B. What is the measure of angle A?

To cut costs, the new manager at Healthy Options wants to mix 4,000 pounds of cat food. The mixture is to have 10% protein. The first ingredient contains 8% protein. The second has 13% protein. How many pounds of the 8% protein ingredient is needed?

Graph the system of Inequalities and show the solution set. Label the corner point. y>5x-5 y<2x-2

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

In the graph of y ≥\geq≥ 1, x ≤\leq≤ 0 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. 4x−y=174 x - y = 174x−y=17

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) 2x+y=4 2y+x=4

Graph the system of inequalities and show the solution set. {y≤−x−1y≥2x−2\left\{ \begin{array} { l } y \leq - x - 1 \\y \geq 2 x - 2\end{array} \right.{y≤−x−1y≥2x−2​

Identify two appropriate variables, and use the variables to write equations. Use either the elimination method or the substitution method to solve the equation The sum of two numbers is 404040 . There difference is 666 . Find the numbers.

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) y=x+0.04x y=1.04x

A parallelogram has angles A and B as supplementary angles. The measure of angle A is 74 degrees more than angle B. What is the measure of angle A?

Which ordered pairs satisfy the system of inequalities given? y\leqx+4 y\geqx-4

Which ordered pairs satisfy the system of inequalities given? y\leq-x-4 y\geqx

Solve by substitution: 5x-5y=-5 4x+2y=20

Nerine combines walking (at 6 km/hr) and running (at 18 km/hr) in her fitness program. Last week she exercised a total of 10 hours and traveled 108 kilometers. How many hours did she walk?

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Nancy has $3.50. She has only dimes (x) and quarters (y). She has 30 coins altogether.

Solve 10 = m(4) + b for m.

Solve by the elimination method: 2x-4y=6 5x+5y=-15

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Alexandra works for two clients during one month. She works a total of 180 hours during the month. She works 50 hours more for one client (y) than for the other (x).

In the graph of x < 1, y ≥\geq≥ -2, what is the corner point?

A right triangle has angles A and B as complementary angles. The measure of angle A is 8 more than the measure of angle B. What is the measure of angle A?

To cut costs, the new manager at Healthy Options wants to mix 4,000 pounds of cat food. The mixture is to have 10% protein. The first ingredient contains 8% protein. The second has 13% protein. How many pounds of the 8% protein ingredient is needed?

Graph the system of Inequalities and show the solution set. Label the corner point. y>5x-5 y<2x-2

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 $\geq$ 1, x $\leq$ 0 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. $4 x - y = 17$

Graph the system of inequalities and show the solution set. $\left\{ \begin{array} { l } y \leq - x - 1 \\y \geq 2 x - 2\end{array} \right.$

Identify two appropriate variables, and use the variables to write equations. Use either the elimination method or the substitution method to solve the equation The sum of two numbers is $40$ _.There difference is $6$ . Find the numbers.

In the graph of x < 1, y $\geq$ -2, what is the corner point?