Question 1

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{array} { r } 
x - 2 y = 5 \
5 x - 10 y = 3
\end{array}$$

Accepted Answer

A)  (2, 5) 
B)  (2, 10) 
C)  (5, 10) 
D)  (5, 5) 
E)  no solution 
A)  (2, 5) 
B)  (2, 10) 
C)  (5, 10) 
D)  (5, 5) 
E)  no solution

Question 2

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Martina has 58 nickels and dimes. She has $3.10 altogether. She has x nickels and y dimes.

Accepted Answer

A)  y = 58 - x, 0.05x + 0.10y = 3.10 
B)  x + y = 58, 0.05y + 0.10x = 3.10 
C)  $x + y = 58,0.25 x + 0.10 y = 3.10$ 
D)  x - y = 58, 0.05x + 0.10y = 3.10 
E)  $x - y = 58,0.05 y + 0.25 x = 3.10$ 
A)  y = 58 - x, 0.05x + 0.10y = 3.10 
B)  x + y = 58, 0.05y + 0.10x = 3.10 
C)  $x + y = 58,0.25 x + 0.10 y = 3.10$ 
D)  x - y = 58, 0.05x + 0.10y = 3.10 
E)  $x - y = 58,0.05 y + 0.25 x = 3.10$

Question 3

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

Accepted Answer

A)  (5, 4) 
B)  (1, 0) 
C)  (9, 8) 
D)  Dependent 
E)  No solution 
A)  (5, 4) 
B)  (1, 0) 
C)  (9, 8) 
D)  Dependent 
E)  No solution

Question 4

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. $4 x + y = 3$

Accepted Answer

A)  $y = - 3 - 4 x$ 
B)  $y = 3 - 4 x$ 
C)  $y = 4 x + 3$ 
D)  $y = 3 x - 4$ 
E)  $y = 4 x - 3$ 
A)  $y = - 3 - 4 x$ 
B)  $y = 3 - 4 x$ 
C)  $y = 4 x + 3$ 
D)  $y = 3 x - 4$ 
E)  $y = 4 x - 3$

Question 5

Solve by the elimination method: $$\begin{array} { l } 
5 x + 5 y = 30 \
2 x + 2 y = 3
\end{array}$$

Accepted Answer

A)  (5, 1) 
B)  (-10, 16) 
C)  (0, 6) 
D)  (-5, 11) 
E)  No solution 
A)  (5, 1) 
B)  (-10, 16) 
C)  (0, 6) 
D)  (-5, 11) 
E)  No solution

Question 6

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{array} { r } 
x - 2 y = 7 \
2 x + 3 y = 0
\end{array}$$

Accepted Answer

A)  (4, -2) 
B)  (3, -2) 
C)  (5, -2) 
D)  (3, -3) 
E)  (3, -1) 
A)  (4, -2) 
B)  (3, -2) 
C)  (5, -2) 
D)  (3, -3) 
E)  (3, -1)

Question 7

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Larry has 26 nickels and quarters. He has $2.20 altogether. He has x nickels and y quarters.

Accepted Answer

A)  x - y = 26, 0.10y + 0.25x = 2.20 
B)  x + y = 26, 0.10x + 0.25y = 2.20 
C)  x - y = 26, 0.05x + 0.25y = 2.20 
D)  x + y = 26, 0.05y + 0.25x = 2.20 
E)  x = 26 - y, 0.05x + 0.25y = 2.20 
A)  x - y = 26, 0.10y + 0.25x = 2.20 
B)  x + y = 26, 0.10x + 0.25y = 2.20 
C)  x - y = 26, 0.05x + 0.25y = 2.20 
D)  x + y = 26, 0.05y + 0.25x = 2.20 
E)  x = 26 - y, 0.05x + 0.25y = 2.20

Question 8

Graph the system of Inequalities and show the solution set. Label the corner point. $$\begin{array} { l } 
y \geq 3 x - 4 \
y > - x + 4
\end{array}$$

Accepted Answer

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

Question 9

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. A boat travels 12 miles upstream to a fishing spot. The trip takes 1.2 hours. The return trip, downstream, takes 0.8 hour. Find the speed of the current, c.

Accepted Answer

A)  c = 2.0 mph 
B)  c = 2.5 mph 
C)  c = 2.8 mph 
D)  c = 3.0 mph 
E)  c = 3.5 mph 
A)  c = 2.0 mph 
B)  c = 2.5 mph 
C)  c = 2.8 mph 
D)  c = 3.0 mph 
E)  c = 3.5 mph

Question 10

In the graph of x $\geq$ 3, y $\leq$ -2, what is the corner point?

Accepted Answer

A)  (-2, -3) 
B)  (-3, 2) 
C)  (3, -2) 
D)  (-3, -2) 
E)  (-2, 3) 
A)  (-2, -3) 
B)  (-3, 2) 
C)  (3, -2) 
D)  (-3, -2) 
E)  (-2, 3)

Question 11

Find the rate of travel for a fishing boat with a speed of 10 miles per hour (mph) moving downstream with a current of 5 mph.

Accepted Answer

A)  15 mph 
B)  10 mph 
C)  7.5 mph 
D)  5 mph 
E)  -5 mph 
A)  15 mph 
B)  10 mph 
C)  7.5 mph 
D)  5 mph 
E)  -5 mph

Question 12

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Renee cuts a 12-meter hose into two lengths. One piece (x) is 2 meters longer than the other (y). What is the length of each piece?

Accepted Answer

A)  $x + y = 12 , x = y + 2$ 
B)  $x + y = 12 , y = x + 2$ 
C)  x - y = 12, x = y + 2 
D)  y - x = 12, y = x - 2 
E)  x + y = 12, x = y - 2 
A)  $x + y = 12 , x = y + 2$ 
B)  $x + y = 12 , y = x + 2$ 
C)  x - y = 12, x = y + 2 
D)  y - x = 12, y = x - 2 
E)  x + y = 12, x = y - 2

Question 13

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. An airplane flies westbound from Denver to San Francisco (950 miles) with the wind in 3.8 hours. On a return flight against the same wind, the travel time is 5 hours. Find the speed of the wind, w.

Accepted Answer

A)  w = 45 mph 
B)  w = 40 mph 
C)  w = 35 mph 
D)  w = 30 mph 
E)  w = 25 mph 
A)  w = 45 mph 
B)  w = 40 mph 
C)  w = 35 mph 
D)  w = 30 mph 
E)  w = 25 mph

Question 14

Define variables for the measures of angles. Write equations based on the given facts as well as the characteristics of complementary angles and supplementary angles. Solve the given resulting system of equations by elimination. 
a) Two angles are complementary. The measure of one angle is $30 ^ { \circ }$ larger than that of the other.
b) Two angles are supplementary. The measure of one angle is $30 ^ { \circ }$ larger than that of the other.

Accepted Answer

A)  a) $55,35$
b) $100,80$ 
B)  a) $60,30$
b) $100,80$ 
C)  a) $60,30$
b) $105,75$ 
D)  a) $50,40$
b) $95,85$ 
E)  a) $55,35$
b) $95,85$ 
A)  a) $55,35$
b) $100,80$ 
B)  a) $60,30$
b) $100,80$ 
C)  a) $60,30$
b) $105,75$ 
D)  a) $50,40$
b) $95,85$ 
E)  a) $55,35$
b) $95,85$

Question 15

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) $$\begin{array} { l } 
2 x + 2 y = 40 \
y = 30 - x
\end{array}$$

Accepted Answer

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

Question 16

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $$\begin{array} { l } 
y + 100 x = 400 \
y = 100 - 400 x
\end{array}$$

Accepted Answer

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

Question 17

Graph the system of Inequalities and show the solutions set. Label the corner point. $$\begin{array} { l } 
x > - 1 \
y \leq 3
\end{array}$$

Accepted Answer

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

Question 18

At the bookstore, 2 notebooks and 5 pens cost $14.69. At the same time, 6 notebooks and 3 pens cost $32.67. What is the cost of one of each?

Accepted Answer

A)  notebooks = $4.87, pens = $0.99 
B)  notebooks = $4.92, pens = $0.97 
C)  notebooks = $4.97, pens = $0.95 
D)  notebooks = $4.79, pens = $1.31 
E)  notebooks = $4.77, pens = $1.03 
A)  notebooks = $4.87, pens = $0.99 
B)  notebooks = $4.92, pens = $0.97 
C)  notebooks = $4.97, pens = $0.95 
D)  notebooks = $4.79, pens = $1.31 
E)  notebooks = $4.77, pens = $1.03

Question 19

The sum of two numbers is 37. Their difference is 6. Identify two appropriate variables, and use the variables to write equations. Use either the elimination method or substitution method to solve the equations.

Accepted Answer

A)  Twice the larger number is 41. 
B)  Twice the larger number is 43. 
C)  Twice the larger number is 42. 
D)  Twice the smaller number is 30. 
E)  Twice the smaller number is 29. 
A)  Twice the larger number is 41. 
B)  Twice the larger number is 43. 
C)  Twice the larger number is 42. 
D)  Twice the smaller number is 30. 
E)  Twice the smaller number is 29.

Question 20

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{aligned}
4 x - y & = 14 \
2 x - 3 y & = 12
\end{aligned}$$

Accepted Answer

A)  (4, -1) 
B)  (2, -2) 
C)  (3, -2) 
D)  (3, -3) 
E)  (4, -2) 
A)  (4, -1) 
B)  (2, -2) 
C)  (3, -2) 
D)  (3, -3) 
E)  (4, -2)

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. x-2y=5 5x-10y=3

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Martina has 58 nickels and dimes. She has $3.10 altogether. She has x nickels and y dimes.

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

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. $4 x + y = 3$

Solve by the elimination method: 5x+5y=30 2x+2y=3

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. x-2y=7 2x+3y=0

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Larry has 26 nickels and quarters. He has $2.20 altogether. He has x nickels and y quarters.

Graph the system of Inequalities and show the solution set. Label the corner point. y\geq3x-4 y>-x+4

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. A boat travels 12 miles upstream to a fishing spot. The trip takes 1.2 hours. The return trip, downstream, takes 0.8 hour. Find the speed of the current, c.

In the graph of x $\geq$ 3, y $\leq$ -2, what is the corner point?

Find the rate of travel for a fishing boat with a speed of 10 miles per hour (mph) moving downstream with a current of 5 mph.

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Renee cuts a 12-meter hose into two lengths. One piece (x) is 2 meters longer than the other (y). What is the length of each piece?

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) 2x+2y=40 y=30-x

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) y+100x=400 y=100-400x

Graph the system of Inequalities and show the solutions set. Label the corner point. x>-1 y\leq3

At the bookstore, 2 notebooks and 5 pens cost $14.69. At the same time, 6 notebooks and 3 pens cost $32.67. What is the cost of one of each?

The sum of two numbers is 37. Their difference is 6. Identify two appropriate variables, and use the variables to write equations. Use either the elimination method or substitution method to solve the equations.

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. 4x-y =14 2x-3y =12

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

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and VTbI\mathrm { V}_{TbI }VTbI​ entered. x-2y=5 5x-10y=3

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Martina has 58 nickels and dimes. She has $3.10 altogether. She has x nickels and y dimes.

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

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. 4x+y=34 x + y = 34x+y=3

Solve by the elimination method: 5x+5y=30 2x+2y=3

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and VTbI\mathrm { V}_{TbI }VTbI​ entered. x-2y=7 2x+3y=0

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Larry has 26 nickels and quarters. He has $2.20 altogether. He has x nickels and y quarters.

Graph the system of Inequalities and show the solution set. Label the corner point. y\geq3x-4 y>-x+4

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. A boat travels 12 miles upstream to a fishing spot. The trip takes 1.2 hours. The return trip, downstream, takes 0.8 hour. Find the speed of the current, c.

In the graph of x ≥\geq≥ 3, y ≤\leq≤ -2, what is the corner point?

Find the rate of travel for a fishing boat with a speed of 10 miles per hour (mph) moving downstream with a current of 5 mph.

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Renee cuts a 12-meter hose into two lengths. One piece (x) is 2 meters longer than the other (y). What is the length of each piece?

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) 2x+2y=40 y=30-x

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) y+100x=400 y=100-400x

Graph the system of Inequalities and show the solutions set. Label the corner point. x>-1 y\leq3

At the bookstore, 2 notebooks and 5 pens cost $14.69. At the same time, 6 notebooks and 3 pens cost $32.67. What is the cost of one of each?

The sum of two numbers is 37. Their difference is 6. Identify two appropriate variables, and use the variables to write equations. Use either the elimination method or substitution method to solve the equations.

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and VTbI\mathrm { V}_{TbI }VTbI​ entered. 4x-y =14 2x-3y =12

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

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. x-2y=5 5x-10y=3

Decide which variable has a coefficient of 1 or -1, and solve for that variable in terms of the other variable. $4 x + y = 3$

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. x-2y=7 2x+3y=0

In the graph of x $\geq$ 3, y $\leq$ -2, what is the corner point?

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. 4x-y =14 2x-3y =12