Question 1

Solve the system of equations by the substitution method.
-$$\left\{ \begin{array} { r } 
x + y = 6 \
y = 2 x
\end{array} \right.$$

Accepted Answer

A)  $( 2 , - 4 )$ 
B)  $( - 2,4 )$ 
C)  $( - 2 , - 4 )$ 
D)  $( 2,4 )$ 
A)  $( 2 , - 4 )$ 
B)  $( - 2,4 )$ 
C)  $( - 2 , - 4 )$ 
D)  $( 2,4 )$

Question 2

Solve the system of linear equations using matrices.
-$$\left\{ \begin{array} { r r } 
- 3 x - y - 2 z = & - 29 \
- 8 x + 7 y - 7 z = & 3 \
7 x - 3 y + z = & 5
\end{array} \right.$$

Accepted Answer

A)  $( 4,4,9 )$ 
B)  $( - 4,9,8 )$ 
C)  $( 4,9,4 )$ 
D)  $\varnothing$ 
A)  $( 4,4,9 )$ 
B)  $( - 4,9,8 )$ 
C)  $( 4,9,4 )$ 
D)  $\varnothing$

Question 3

Solve.
-The manager of a bulk foods establishment sells a trail mix for $5 per pound and premium cashews for $11 per pound. The manager wishes to make a 120-pound trail mix-cashew mixture that will sell for $9 per pound.
How many pounds of each should be used?

Accepted Answer

A)  100 pounds of trail mix 
B)  60 pounds of trail mix 20 pounds of cashews 60 pounds of cashews 
C)  80 pounds of trail mix 
D)  40 pounds of trail mix 40 pounds of cashews 80 pounds of cashews 
A)  100 pounds of trail mix 
B)  60 pounds of trail mix 20 pounds of cashews 60 pounds of cashews 
C)  80 pounds of trail mix 
D)  40 pounds of trail mix 40 pounds of cashews 80 pounds of cashews

Question 4

Solve the system of equations.
-$$\left\{ \begin{array} { l } 
\frac { x } { 3 } + \frac { y } { 9 } = 1 \
\frac { x } { 2 } - \frac { y } { 6 } = 0
\end{array} \right.$$

Accepted Answer

A)  $\left( \frac { 3 } { 2 } , \frac { 9 } { 2 } \right)$ 
B)  $\left( \frac { 9 } { 2 } , \frac { 3 } { 2 } \right)$ 
C)  $\left\{ ( x , y ) \mid \frac { x } { 3 } + \frac { y } { 9 } = 1 \right\}$ 
D)  $\varnothing$ 
A)  $\left( \frac { 3 } { 2 } , \frac { 9 } { 2 } \right)$ 
B)  $\left( \frac { 9 } { 2 } , \frac { 3 } { 2 } \right)$ 
C)  $\left\{ ( x , y ) \mid \frac { x } { 3 } + \frac { y } { 9 } = 1 \right\}$ 
D)  $\varnothing$

Question 5

Solve the system of equations.
-$$\left\{ \begin{aligned}
5 x + 3 y & = - 7 \
x & = - 2 y
\end{aligned} \right.$$

Accepted Answer

A)  $( 1 , - 2 )$ 
B)  $( - 2,1 )$ 
C)  $\{ ( x , y ) \mid 5 x + 3 y = - 7 \}$ 
D)  $\varnothing$ 
A)  $( 1 , - 2 )$ 
B)  $( - 2,1 )$ 
C)  $\{ ( x , y ) \mid 5 x + 3 y = - 7 \}$ 
D)  $\varnothing$

Question 6

Solve the system by graphing.
$\left\{\begin{array}{l}
-x+4 y=-16 \
2 x-8 y=8
\end{array}\right.$

Accepted Answer

A)  (-4, -1) 
B)  (0, -1) 
C)  (0, -4) 
D)  $\phi$ 
A)  (-4, -1) 
B)  (0, -1) 
C)  (0, -4) 
D)  $\phi$

Question 7

Solve the system.
-$$\left\{ \begin{array} { c } 
x - y + 4 z = - 2 \
4 x + z = 0 \
- x + y - 4 z = 4
\end{array} \right.$$

Accepted Answer

A)  $( 0,2,0 )$ 
B)  $( 0,0,2 )$ 
C)  $\varnothing$ 
D)  $( 4,2,0 )$ 
A)  $( 0,2,0 )$ 
B)  $( 0,0,2 )$ 
C)  $\varnothing$ 
D)  $( 4,2,0 )$

Question 8

Solve the system of equations.
-$$\left\{ \begin{array} { l } 
\frac { x + 5 } { 2 } = \frac { y + 15 } { 4 } \
\frac { x } { 4 } = \frac { 2 y + 6 } { 8 }
\end{array} \right.$$

Accepted Answer

A)  $( - 1,2 )$ 
B)  $( 2 , - 1 )$ 
C)  $\left\{ ( x , y ) \mid \frac { x + 5 } { 2 } = \frac { y + 15 } { 4 } \right\}$ 
D)  $\varnothing$ 
A)  $( - 1,2 )$ 
B)  $( 2 , - 1 )$ 
C)  $\left\{ ( x , y ) \mid \frac { x + 5 } { 2 } = \frac { y + 15 } { 4 } \right\}$ 
D)  $\varnothing$

Question 9

Solve the system of equations by the elimination method.
-$$\left\{ \begin{array} { l } 
4 x + y = 19 \
3 x + 4 y = - 2
\end{array} \right.$$

Accepted Answer

A)  $( - 5,6 )$ 
B)  $( 6 , - 5 )$ 
C)  $( 0 , - 5 )$ 
D)  $\varnothing$ 
A)  $( - 5,6 )$ 
B)  $( 6 , - 5 )$ 
C)  $( 0 , - 5 )$ 
D)  $\varnothing$

Question 10

Solve the system.
-$$\left\{ \begin{array} { r } 
x - y + 3 z = - 2 \
3 x + z = 0 \
- x + y - 3 z = 10
\end{array} \right.$$

Accepted Answer

A)  $( 3,2,0 )$ 
B)  $( 0,0,2 )$ 
C)  $( 0,2,0 )$ 
D)  $\varnothing$ 
A)  $( 3,2,0 )$ 
B)  $( 0,0,2 )$ 
C)  $( 0,2,0 )$ 
D)  $\varnothing$

Question 11

Solve the system of equations by the elimination method.
-$$\left\{ \begin{array} { r } 
2 x + 10 y = - 48 \
12 x + 2 y = 60
\end{array} \right.$$

Accepted Answer

A)  $( 6 , - 6 )$ 
B)  $( 12 , - 12 )$ 
C)  $( - 6,6 )$ 
D)  $( - 2,6 )$ 
A)  $( 6 , - 6 )$ 
B)  $( 12 , - 12 )$ 
C)  $( - 6,6 )$ 
D)  $( - 2,6 )$

Question 12

Solve the system.
-$$\left\{ \begin{array} { l } 
3 x + 3 y + z = 2 \
5 x - 5 y - z = - 16 \
4 x + y + 5 z = - 21
\end{array} \right.$$

Accepted Answer

A)  $( - 4,3 , - 1 )$ 
B)  $( - 1 , - 4,3 )$ 
C)  $( - 1,3 , - 4 )$ 
D)  $\varnothing$ 
A)  $( - 4,3 , - 1 )$ 
B)  $( - 1 , - 4,3 )$ 
C)  $( - 1,3 , - 4 )$ 
D)  $\varnothing$

Question 13

Solve.
-A certain aircraft can fly 1190 miles with the wind in 5 hours and travel the same distance against the wind in 7 hours. What is the speed of the wind?

Accepted Answer

A)  17 mph 
B)  34 mph 
C)  68 mph 
D)  51 mph 
A)  17 mph 
B)  34 mph 
C)  68 mph 
D)  51 mph

Question 14

Graph the solution of the system of linear inequalities.
-$\left\{ \begin{array} { l } 
y \leq 3 x - 1 \
y \geq - 3 - x
\end{array} \right.$

Accepted Answer

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

Question 15

Solve the system.
-$$\left\{ \begin{array} { r } 
x - y + 4 z = - 8 \
5 x + z = - 1 \
x + 4 y + z = 15
\end{array} \right.$$

Accepted Answer

A)  $( - 1,4,0 )$ 
B)  $( - 1,0,4 )$ 
C)  $( 0,4 , - 1 )$ 
D)  $\varnothing$ 
A)  $( - 1,4,0 )$ 
B)  $( - 1,0,4 )$ 
C)  $( 0,4 , - 1 )$ 
D)  $\varnothing$

Question 16

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l } 
\text { matrix consistent system of equations triple } \
\text { solution inconsistent element } \
\text { column }
\end{array}$$
-The numbers aligned horizontally in a matrix are in the same .

Accepted Answer

A)  element 
B)  row 
C) solution 
D)  column 
A)  element 
B)  row 
C) solution 
D)  column

Question 17

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

Accepted Answer

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

Question 18

Solve the system of equations.
-$$\left\{ \begin{array} { l } 
y = 3 x + 2 \
y = 8 x + 1
\end{array} \right.$$

Accepted Answer

A)  $\left( \frac { 1 } { 5 } , \frac { 13 } { 5 } \right)$ 
B)  $\left( \frac { 13 } { 5 } , \frac { 1 } { 5 } \right)$ 
C)  $\{ ( x , y ) \mid y = 3 x + 2 \}$ 
D)  $\varnothing$ 
A)  $\left( \frac { 1 } { 5 } , \frac { 13 } { 5 } \right)$ 
B)  $\left( \frac { 13 } { 5 } , \frac { 1 } { 5 } \right)$ 
C)  $\{ ( x , y ) \mid y = 3 x + 2 \}$ 
D)  $\varnothing$

Question 19

Solve the system.
-$$\left\{ \begin{aligned}
x - y + 3 z & = 0 \
4 x + z & = 1 \
x + 5 y + z & = 16
\end{aligned} \right.$$

Accepted Answer

A)  $( 0,3,1 )$ 
B)  $( 1,3,0 )$ 
C)  $( 1,0,3 )$ 
D)  $\varnothing$ 
A)  $( 0,3,1 )$ 
B)  $( 1,3,0 )$ 
C)  $( 1,0,3 )$ 
D)  $\varnothing$

Question 20

Solve the system.
-$$\left\{ \begin{aligned}
x + y + z & = - 5 \
x - y + 4 z & = - 18 \
2 x + 2 y + 2 z & = - 4
\end{aligned} \right.$$

Accepted Answer

A)  $( 1 , - 1 , - 5 )$ 
B)  $( - 5,1 , - 1 )$ 
C)  $( - 5 , - 1,1 )$ 
D)  $\varnothing$ 
A)  $( 1 , - 1 , - 5 )$ 
B)  $( - 5,1 , - 1 )$ 
C)  $( - 5 , - 1,1 )$ 
D)  $\varnothing$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { r } x + y = 6 \\y = 2 x\end{array} \right.$

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { r r } - 3 x - y - 2 z = & - 29 \\- 8 x + 7 y - 7 z = & 3 \\7 x - 3 y + z = & 5\end{array} \right.$

Solve. -The manager of a bulk foods establishment sells a trail mix for $5 per pound and premium cashews for $11 per pound. The manager wishes to make a 120-pound trail mix-cashew mixture that will sell for $9 per pound. How many pounds of each should be used?

Solve the system of equations. - $\left\{ \begin{array} { l } \frac { x } { 3 } + \frac { y } { 9 } = 1 \\\frac { x } { 2 } - \frac { y } { 6 } = 0\end{array} \right.$

Solve the system of equations. - $\left\{ \begin{aligned}5 x + 3 y & = - 7 \\x & = - 2 y\end{aligned} \right.$

Solve the system by graphing. $\left\{\begin{array}{l}-x+4 y=-16 \\2 x-8 y=8\end{array}\right.$ $Solve the system by graphing. \left\{\begin{array}{l} -x+4 y=-16 \\ 2 x-8 y=8 \end{array}\right.$

Solve the system. - $\left\{ \begin{array} { c } x - y + 4 z = - 2 \\4 x + z = 0 \\- x + y - 4 z = 4\end{array} \right.$

Solve the system of equations. - $\left\{ \begin{array} { l } \frac { x + 5 } { 2 } = \frac { y + 15 } { 4 } \\\frac { x } { 4 } = \frac { 2 y + 6 } { 8 }\end{array} \right.$

Solve the system of equations by the elimination method. - $\left\{ \begin{array} { l } 4 x + y = 19 \\3 x + 4 y = - 2\end{array} \right.$

Solve the system. - $\left\{ \begin{array} { r } x - y + 3 z = - 2 \\3 x + z = 0 \\- x + y - 3 z = 10\end{array} \right.$

Solve the system of equations by the elimination method. - $\left\{ \begin{array} { r } 2 x + 10 y = - 48 \\12 x + 2 y = 60\end{array} \right.$

Solve the system. - $\left\{ \begin{array} { l } 3 x + 3 y + z = 2 \\5 x - 5 y - z = - 16 \\4 x + y + 5 z = - 21\end{array} \right.$

Solve. -A certain aircraft can fly 1190 miles with the wind in 5 hours and travel the same distance against the wind in 7 hours. What is the speed of the wind?

Graph the solution of the system of linear inequalities. - $\left\{ \begin{array} { l } y \leq 3 x - 1 \\y \geq - 3 - x\end{array} \right.$ $Graph the solution of the system of linear inequalities. - \left\{ \begin{array} { l } y \leq 3 x - 1 \\ y \geq - 3 - x \end{array} \right.$

Solve the system. - $\left\{ \begin{array} { r } x - y + 4 z = - 8 \\5 x + z = - 1 \\x + 4 y + z = 15\end{array} \right.$

Fill in the blank with one of the words or phrases listed below. matrix consistent system of equations triple solution inconsistent element column -The numbers aligned horizontally in a matrix are in the same .

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

Solve the system of equations. - $\left\{ \begin{array} { l } y = 3 x + 2 \\y = 8 x + 1\end{array} \right.$

Solve the system. - $\left\{ \begin{aligned}x - y + 3 z & = 0 \\4 x + z & = 1 \\x + 5 y + z & = 16\end{aligned} \right.$

Solve the system. - $\left\{ \begin{aligned}x + y + z & = - 5 \\x - y + 4 z & = - 18 \\2 x + 2 y + 2 z & = - 4\end{aligned} \right.$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 4: Systems of Equations and Inequalities

Solve the system of equations by the substitution method. - {x+y=6y=2x\left\{ \begin{array} { r } x + y = 6 \\y = 2 x\end{array} \right.{x+y=6y=2x​

Solve the system of linear equations using matrices. - {−3x−y−2z=−29−8x+7y−7z=37x−3y+z=5\left\{ \begin{array} { r r } - 3 x - y - 2 z = & - 29 \\- 8 x + 7 y - 7 z = & 3 \\7 x - 3 y + z = & 5\end{array} \right.⎩⎨⎧​−3x−y−2z=−8x+7y−7z=7x−3y+z=​−2935​

Solve. -The manager of a bulk foods establishment sells a trail mix for $5 per pound and premium cashews for $11 per pound. The manager wishes to make a 120-pound trail mix-cashew mixture that will sell for $9 per pound. How many pounds of each should be used?

Solve the system of equations. - {x3+y9=1x2−y6=0\left\{ \begin{array} { l } \frac { x } { 3 } + \frac { y } { 9 } = 1 \\\frac { x } { 2 } - \frac { y } { 6 } = 0\end{array} \right.{3x​+9y​=12x​−6y​=0​

Solve the system of equations. - {5x+3y=−7x=−2y\left\{ \begin{aligned}5 x + 3 y & = - 7 \\x & = - 2 y\end{aligned} \right.{5x+3yx​=−7=−2y​

Solve the system by graphing. {−x+4y=−162x−8y=8\left\{\begin{array}{l}-x+4 y=-16 \\2 x-8 y=8\end{array}\right.{−x+4y=−162x−8y=8​

Solve the system. - {x−y+4z=−24x+z=0−x+y−4z=4\left\{ \begin{array} { c } x - y + 4 z = - 2 \\4 x + z = 0 \\- x + y - 4 z = 4\end{array} \right.⎩⎨⎧​x−y+4z=−24x+z=0−x+y−4z=4​

Solve the system of equations. - {x+52=y+154x4=2y+68\left\{ \begin{array} { l } \frac { x + 5 } { 2 } = \frac { y + 15 } { 4 } \\\frac { x } { 4 } = \frac { 2 y + 6 } { 8 }\end{array} \right.{2x+5​=4y+15​4x​=82y+6​​

Solve the system of equations by the elimination method. - {4x+y=193x+4y=−2\left\{ \begin{array} { l } 4 x + y = 19 \\3 x + 4 y = - 2\end{array} \right.{4x+y=193x+4y=−2​

Solve the system. - {x−y+3z=−23x+z=0−x+y−3z=10\left\{ \begin{array} { r } x - y + 3 z = - 2 \\3 x + z = 0 \\- x + y - 3 z = 10\end{array} \right.⎩⎨⎧​x−y+3z=−23x+z=0−x+y−3z=10​

Solve the system of equations by the elimination method. - {2x+10y=−4812x+2y=60\left\{ \begin{array} { r } 2 x + 10 y = - 48 \\12 x + 2 y = 60\end{array} \right.{2x+10y=−4812x+2y=60​

Solve the system. - {3x+3y+z=25x−5y−z=−164x+y+5z=−21\left\{ \begin{array} { l } 3 x + 3 y + z = 2 \\5 x - 5 y - z = - 16 \\4 x + y + 5 z = - 21\end{array} \right.⎩⎨⎧​3x+3y+z=25x−5y−z=−164x+y+5z=−21​