Question 1

Solve.
-$$\begin{array} { l } 
x - y + z = 8 \
x + y + z = 6 \
x + y - z = - 12
\end{array}$$

Accepted Answer

A)  $( 2 , - 1 , - 9 )$ 
B)  $( - 2 , - 1 , - 9 )$ 
C)  $( 2 , - 1,9 )$ 
D)  $( - 2 , - 1,9 )$ 
A)  $( 2 , - 1 , - 9 )$ 
B)  $( - 2 , - 1 , - 9 )$ 
C)  $( 2 , - 1,9 )$ 
D)  $( - 2 , - 1,9 )$

Question 2

Use the substitution method to solve the system.
-$$\begin{array} { l } 
\frac { 3 } { 5 } x + \frac { 2 } { 3 } y = - 13 \
- \frac { 3 } { 5 } x + 3 y = 24
\end{array}$$

Accepted Answer

A)  $( - 25,4 )$ 
B)  $( - 15 , - 11 )$ 
C)  $( - 15 , - 6 )$ 
D)  $( - 25,3 )$ 
A)  $( - 25,4 )$ 
B)  $( - 15 , - 11 )$ 
C)  $( - 15 , - 6 )$ 
D)  $( - 25,3 )$

Question 3

Solve the system of equations.
-$$\begin{array} { r l r } 
x - y + 5 z & = & - 4 \
3 x + z & = & 0 \
- x + y - 5 z & = & 12
\end{array}$$

Accepted Answer

A)  $( 0,0,4 )$ 
B)  $( 5,4,0 )$ 
C)  No solution 
D)  Infinite number of solutions; dependent equations 
A)  $( 0,0,4 )$ 
B)  $( 5,4,0 )$ 
C)  No solution 
D)  Infinite number of solutions; dependent equations

Question 4

Graph the system of inequalities.
-$\begin{array}{l}
3 x-2 y \leq 6 \
x-1>0
\end{array}$

Accepted Answer

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

Question 5

Use the substitution method to solve the system.
-x - 7y = 36 5x - 8y = 45

Accepted Answer

A) (1, -5) 
B) (-1, -4) 
C) (0, -4) 
D) No solution 
A) (1, -5) 
B) (-1, -4) 
C) (0, -4) 
D) No solution

Question 6

Solve.
-$$\begin{aligned}
x + 3 y + 2 z & = 23 \
2 y + 3 z & = 23 \
z & = 5
\end{aligned}$$
$( 5,4,1 )$

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 7

Graph the system of inequalities.
-$\begin{array}{l}
y>-2 \
x \geq 1
\end{array}$

Accepted Answer

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

Question 8

Solve the system of equations.
-$$\begin{array} { l } 
x - y + 3 z = - 4 \
4 x + z = - 1 \
x + 4 y + z = 3
\end{array}$$

Accepted Answer

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

Question 9

Solve.
-A couple have bought a new house and are comparing quotes from two moving companies for moving their furniture. Company A charges $\$ 110$ for the truck and $\$ 60$ per hour for the movers. Company B charges $\$ 90$ for the truck and $\$ 75$ 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)  $60 y = x + 110$
$75 y = x + 90$ 
B)  $60 \mathrm { y } = 110 \mathrm { x }$
$75 \mathrm { y } = 90 \mathrm { x }$ 
C)  $y = 110 x + 60$
$y = 90 x + 75$ 
D)  $y = 60 x + 110$
$y = 75 x + 90$ 
A)  $60 y = x + 110$
$75 y = x + 90$ 
B)  $60 \mathrm { y } = 110 \mathrm { x }$
$75 \mathrm { y } = 90 \mathrm { x }$ 
C)  $y = 110 x + 60$
$y = 90 x + 75$ 
D)  $y = 60 x + 110$
$y = 75 x + 90$

Question 10

Graph the system of inequalities.
-$\begin{array}{l}
2 x+3 y \leq 6 \
x-y \leq 3 \
y \leq 2
\end{array}$

Accepted Answer

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

Question 11

Graph the system of inequalities.
-$2 x + y \geq 4$
$x - 1 > 0$

Accepted Answer

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

Question 12

Solve the problem.
-A textile company has specific dyeing and drying times for its different cloths. A roll of Cloth A requires 55 minutes of dyeing time and 45 minutes of drying time. A roll of Cloth B requires 60 minutes of dyeing time and
30 minutes of drying time. The production division allocates 2280 minutes of dyeing time and 1560 minutes of
Drying time for the week. How many rolls of each cloth can be dyed and dried?

Accepted Answer

A) 13 rolls of Cloth A, 28 rolls of Cloth B 
B) 24 rolls of Cloth A, 16 rolls of Cloth B 
C) 2 rolls of Cloth A, 49 rolls of Cloth B 
D) 13 rolls of Cloth A, 40 rolls of Cloth B 
A) 13 rolls of Cloth A, 28 rolls of Cloth B 
B) 24 rolls of Cloth A, 16 rolls of Cloth B 
C) 2 rolls of Cloth A, 49 rolls of Cloth B 
D) 13 rolls of Cloth A, 40 rolls of Cloth B

Question 13

Solve the system by graphing.
-3x + 3y = 27 2x - 2y = -2

Accepted Answer

A)  $x = 5 , y = 4$ 
B)  $x = 3 , y = - 8$ 
C)  $x = 4 , y = 5$ 
D)  no solution 
A)  $x = 5 , y = 4$ 
B)  $x = 3 , y = - 8$ 
C)  $x = 4 , y = 5$ 
D)  no solution

Question 14

If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why.
--8x + 6y = -80 -3x - 9y = 60

Accepted Answer

A) (4, -8) 
B) (-4, -7) 
C) (3, -7) 
D) No solution; inconsistent system of equations 
A) (4, -8) 
B) (-4, -7) 
C) (3, -7) 
D) No solution; inconsistent system of equations

Question 15

Solve using a system of three linear equations.
-A total of 384 people attend a community theatre performance. The admission prices were $10.00 for adults, $8.00 for students, and $9.00 for senior citizens. The ticket sales totaled $3590. At the theatre's next board
Meeting, the finance manager proposed that for the next play they raise prices to $11.00 for adults, $8.50 for
Students, and $9.50 for senior citizens. He said that if the exact same number of people attend the next
Performance, the ticket sales would be $3886. How many adults, students, and senior citizens attended the
Play?

Accepted Answer

A) 196 adults, 78 students, 110 senior citizens 
B) 200 adults, 80 students, 104 senior citizens 
C) 204 adults, 72 students, 108 senior citizens 
D) 208 adults, 74 students, 102 senior citizens 
A) 196 adults, 78 students, 110 senior citizens 
B) 200 adults, 80 students, 104 senior citizens 
C) 204 adults, 72 students, 108 senior citizens 
D) 208 adults, 74 students, 102 senior citizens

Question 16

Solve the problem.
-A twin-engined aircraft can fly 768 miles from city A to city B in 3 hours with the wind and make the return trip in 8 hours against the wind. What is the speed of the wind?

Accepted Answer

A) 112 mph 
B) 96 mph 
C) 80 mph 
D) 64 mph 
A) 112 mph 
B) 96 mph 
C) 80 mph 
D) 64 mph

Question 17

Find the solution to the system by addition (elimination) method.
-6x + 5y = -19 -6x - 11y = 49

Accepted Answer

A) (6, 5) 
B) (1, -5) 
C) (-1, 5) 
D) (-6, - 5) 
A) (6, 5) 
B) (1, -5) 
C) (-1, 5) 
D) (-6, - 5)

Question 18

Solve.
-$$\begin{array} { l } 
x + y + z = - 2 \
x - y + 5 z = - 26 \
4 x + y + z = 1 \
1,2 , - 5 )
\end{array}$$

Accepted Answer

A)  $\mathrm { No }$ 
B)  Yes 
A)  $\mathrm { No }$ 
B)  Yes

Question 19

Solve.
-Juanita is having her yard landscaped. She obtained an estimate from two landscaping companies. Company A gave an estimate of $180 for materials and equipment rental plus $60 per hour for labor. Company B gave and
Estimate of $300 for materials and equipment rental plus $45 per hour for labor. Create a cost equation for each
Company where y is the total cost of the landscaping and x is the number of hours of labor. Determine how
Many hours of labor will be required for the two companies to cost the same.

Accepted Answer

A) 7 hours 
B) 11 hours 
C) 8 hours 
D) 12 hours 
A) 7 hours 
B) 11 hours 
C) 8 hours 
D) 12 hours

Question 20

Solve using a system of three linear equations.
-A real estate investor is examining a triangular plot of land. She measures each angle of the field. The sum of the first and second angles is 114° more than the measure of the third angle. If the measure of the third angle is
Subtracted from the measure of the second angle, the result is twice the measure of the first angle. Find the
Measure of each angle. (Note: The sum of the angles of a triangle is 180°.)

Accepted Answer

A) First angle is 42°, second angle is 111°, third angle is 27° 
B) First angle is 38°, second angle is 109°, third angle is 33° 
C) First angle is 36°, second angle is 109°, third angle is 31° 
D) First angle is 44°, second angle is 105°, third angle is 31° 
A) First angle is 42°, second angle is 111°, third angle is 27° 
B) First angle is 38°, second angle is 109°, third angle is 33° 
C) First angle is 36°, second angle is 109°, third angle is 31° 
D) First angle is 44°, second angle is 105°, third angle is 31°

Solve. - x-y+z=8 x+y+z=6 x+y-z=-12

Use the substitution method to solve the system. - x+y=-13 -x+3y=24

Solve the system of equations. - x-y+5z = -4 3x+z = 0 -x+y-5z = 12

Graph the system of inequalities. - 3x-2y\leq6 x-1>0 $Graph the system of inequalities. - \begin{array}{l} 3 x-2 y \leq 6 \\ x-1>0 \end{array}$

Use the substitution method to solve the system. -x - 7y = 36 5x - 8y = 45

Solve. - x+3y+2z =23 2y+3z =23 z =5 $( 5,4,1 )$

Graph the system of inequalities. - y>-2 x\geq1 $Graph the system of inequalities. - \begin{array}{l} y>-2 \\ x \geq 1 \end{array}$

Solve the system of equations. - x-y+3z=-4 4x+z=-1 x+4y+z=3

Graph the system of inequalities. - 2x+3y\leq6 x-y\leq3 y\leq2 $Graph the system of inequalities. - \begin{array}{l} 2 x+3 y \leq 6 \\ x-y \leq 3 \\ y \leq 2 \end{array}$

Graph the system of inequalities. - $2 x + y \geq 4$ $x - 1 > 0$ $Graph the system of inequalities. - 2 x + y \geq 4 x - 1 > 0$

Solve the system by graphing. -3x + 3y = 27 2x - 2y = -2

If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why. --8x + 6y = -80 -3x - 9y = 60

Solve the problem. -A twin-engined aircraft can fly 768 miles from city A to city B in 3 hours with the wind and make the return trip in 8 hours against the wind. What is the speed of the wind?

Find the solution to the system by addition (elimination) method. -6x + 5y = -19 -6x - 11y = 49

Solve. - x+y+z=-2 x-y+5z=-26 4x+y+z=1 1,2,-5)

Real Numbers and Variables

Equations, Inequalities, and Applications

Graphing and Functions

Exponents and Polynomials

Factoring

Rational Expressions and Equations

Rational Exponents and Radicals

Quadratic Equations and Inequalities

The Conic Sections

Additional Properties of Functions

Logarithmic and Exponential Functions

Filters

Exam 4: Systems of Linear Equations and Inequalities

Solve. - x-y+z=8 x+y+z=6 x+y-z=-12

Use the substitution method to solve the system. - x+y=-13 -x+3y=24

Solve the system of equations. - x-y+5z = -4 3x+z = 0 -x+y-5z = 12

Graph the system of inequalities. - 3x-2y\leq6 x-1>0

Use the substitution method to solve the system. -x - 7y = 36 5x - 8y = 45

Solve. - x+3y+2z =23 2y+3z =23 z =5 (5,4,1)( 5,4,1 )(5,4,1)

Graph the system of inequalities. - y>-2 x\geq1

Solve the system of equations. - x-y+3z=-4 4x+z=-1 x+4y+z=3

Graph the system of inequalities. - 2x+3y\leq6 x-y\leq3 y\leq2

Graph the system of inequalities. - 2x+y≥42 x + y \geq 42x+y≥4 x−1>0x - 1 > 0x−1>0

Solve the system by graphing. -3x + 3y = 27 2x - 2y = -2

If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why. --8x + 6y = -80 -3x - 9y = 60

Solve the problem. -A twin-engined aircraft can fly 768 miles from city A to city B in 3 hours with the wind and make the return trip in 8 hours against the wind. What is the speed of the wind?

Find the solution to the system by addition (elimination) method. -6x + 5y = -19 -6x - 11y = 49

Solve. - x+y+z=-2 x-y+5z=-26 4x+y+z=1 1,2,-5)

Real Numbers and Variables

Equations, Inequalities, and Applications

Graphing and Functions

Exponents and Polynomials

Factoring

Rational Expressions and Equations

Rational Exponents and Radicals

Quadratic Equations and Inequalities

The Conic Sections

Additional Properties of Functions

Logarithmic and Exponential Functions

Filters

Graph the system of inequalities. - 3x-2y\leq6 x-1>0 $Graph the system of inequalities. - \begin{array}{l} 3 x-2 y \leq 6 \\ x-1>0 \end{array}$

Solve. - x+3y+2z =23 2y+3z =23 z =5 $( 5,4,1 )$

Graph the system of inequalities. - y>-2 x\geq1 $Graph the system of inequalities. - \begin{array}{l} y>-2 \\ x \geq 1 \end{array}$

Graph the system of inequalities. - 2x+3y\leq6 x-y\leq3 y\leq2 $Graph the system of inequalities. - \begin{array}{l} 2 x+3 y \leq 6 \\ x-y \leq 3 \\ y \leq 2 \end{array}$

Graph the system of inequalities. - $2 x + y \geq 4$ $x - 1 > 0$ $Graph the system of inequalities. - 2 x + y \geq 4 x - 1 > 0$