Question 1

Solve.
-$\begin{aligned} x + 5 y + 3 z & = - 22 \ 5 y + 4 z & = - 30 \ z & = - 5 \ ( 3 , - 2 , - 5 ) \end{aligned}$

Accepted Answer

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

Question 2

Solve.
-$$\begin{array} { l } 
x + y + z = 7 \
x - y + 2 z = 7 \
5 x + y + z = 11
\end{array}$$

Accepted Answer

A)  $( 1,4,2 )$ 
B)  $( 4,2,1 )$ 
C)  $( 1,2,4 )$ 
D)  $( 4,1,2 )$ 
A)  $( 1,4,2 )$ 
B)  $( 4,2,1 )$ 
C)  $( 1,2,4 )$ 
D)  $( 4,1,2 )$

Question 3

Graph the system of inequalities.
-$$\begin{array} { l } 
2 x + y \leq 4 \
y - 1 < 0
\end{array}$$

Accepted Answer

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

Question 4

Solve the system of equations. If there is no solution to the system, give a reason.
-$$\begin{array} { c } 
x - 6 y = 4 \
6 x - 5 y = 24
\end{array}$$

Accepted Answer

A)  No solution; Inconsistent system of equations 
B)  $( 5,4 )$ 
C)  $( 4,0 )$ 
D)  $( - 4 , - 1 )$ 
A)  No solution; Inconsistent system of equations 
B)  $( 5,4 )$ 
C)  $( 4,0 )$ 
D)  $( - 4 , - 1 )$

Question 5

Find the solution to the system by addition (elimination) method.
-2x + 10y = -56 9x + 2y = 49

Accepted Answer

A) (9, -9) 
B) (7, -7) 
C) (-7, 7) 
D) (-2, 7) 
A) (9, -9) 
B) (7, -7) 
C) (-7, 7) 
D) (-2, 7)

Question 6

Find the solution to the system by addition (elimination) method.
-x + y = -6 x - y = 14

Accepted Answer

A) (6, 4) 
B) (4, 10) 
C) (4, -10) 
D) (6, -10) 
A) (6, 4) 
B) (4, 10) 
C) (4, -10) 
D) (6, -10)

Question 7

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

Accepted Answer

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

Question 8

If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why.
-4x = 45 - 9y -2x + 7y = -11

Accepted Answer

A) (8, 2) 
B) No solution; inconsistent system of equations 
C) (9, 1) 
D) (9, 2) 
A) (8, 2) 
B) No solution; inconsistent system of equations 
C) (9, 1) 
D) (9, 2)

Question 9

Solve the problem.
-A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 7 soft drinks for $42.00. The second group bought 7 slices of pizza and 6 soft drinks for $
36)57. How much does one slice of pizza cost?

Accepted Answer

A) $1.44 per slice of pizza 
B) $1.94 per slice of pizza 
C) $3.49 per slice of pizza 
D) $3.99 per slice of pizza 
A) $1.44 per slice of pizza 
B) $1.94 per slice of pizza 
C) $3.49 per slice of pizza 
D) $3.99 per slice of pizza

Question 10

Find the solution to the system by addition (elimination) method.
-$$\frac { 1 } { 3 } x + \frac { 1 } { 3 } y = - 4$$
$x - y = - 2$

Accepted Answer

A)  $( - 7 , - 5 )$ 
B)  $( 7 , - 4 )$ 
C)  $( - 8 , - 4 )$ 
D)  No solution 
A)  $( - 7 , - 5 )$ 
B)  $( 7 , - 4 )$ 
C)  $( - 8 , - 4 )$ 
D)  No solution

Question 11

Solve.
-A bakery plans to market a mixed assortment of its two most popular cookies: Chocolate Chip and Toffee Chunk. Their marketing analyst proposes that the new assortment be constrained by the inequality $3 \mathrm { C } + 4 \mathrm {~T} \leq 31$, where $\mathrm { C }$ is the number of Chocolate Chip cookies and $\mathrm { T }$ is the number of Toffee Chunk cookies. Their sales analyst suggests in order to offer a reasonably priced product the assortment should be constrained by the inequality $5 \mathrm { C } + 2 \mathrm {~T} \leq 33$. The number of each type of cookie cannot be negative, so $\mathrm { C } \geq 0$ and $\mathrm { T } \geq 0$. Graph the region satisfying all the requirements for the assortment using $\mathrm { C }$ as the horizontal axis and $\mathrm { T }$ as the vertical axis. Does the combination of 6 Chocolate Chip cookies and 3 Toffee Chunk cookies satisfy all of the requirements?

Accepted Answer

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

Question 12

Solve the system by graphing.
-3x - 2y = 4 -6x + 4y = 7

Accepted Answer

A)  $x = 2 , y = 1$ 
B)  no solution 
C)  infinite number of solutions 
D)  $x = 1 , y = 2$ 
A)  $x = 2 , y = 1$ 
B)  no solution 
C)  infinite number of solutions 
D)  $x = 1 , y = 2$

Question 13

Graph the system of inequalities.
-$y \leq 2 x + 4$
$y > - \frac { 3 } { 4 } x$

Accepted Answer

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

Question 14

Solve the system by graphing.
-3x + y = 12 9x + 3y = 36

Accepted Answer

A)  infinite number of solutions 
B)  no solution 
C)  $x = 5 , y = - 3$ 
D)  $x = 0 , y = 12$ 
A)  infinite number of solutions 
B)  no solution 
C)  $x = 5 , y = - 3$ 
D)  $x = 0 , y = 12$

Question 15

Find the solution to the system by addition (elimination) method.
-5x + 54y = 54 3x - 6y = -6

Accepted Answer

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

Question 16

Solve the problem.
-Sandy Brondello scored 24 points in a recent basketball game without making any 3-point shots. She scored 16 times, making several free throws worth 1 point each and several field goals worth two points each. How many
Free throws did she make? How many 2-point field goals did she make?

Accepted Answer

A) 10 free throws, 7 field goals 
B) 6 free throws, 10 field goals 
C) 9 free throws, 7 field goals 
D) 8 free throws, 8 field goals 
A) 10 free throws, 7 field goals 
B) 6 free throws, 10 field goals 
C) 9 free throws, 7 field goals 
D) 8 free throws, 8 field goals

Question 17

Use the substitution method to solve the system.
-x + 6y = 6 4x - 5y = -5

Accepted Answer

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

Question 18

Solve the system by graphing.
-x = -y y + x = 6

Accepted Answer

A)  no solution 
B)  infinite number of solutions 
C)  $x = 1 , y = 5$ 
D)  $x = 1 , y = 1$ 
A)  no solution 
B)  infinite number of solutions 
C)  $x = 1 , y = 5$ 
D)  $x = 1 , y = 1$

Question 19

Graph the system of inequalities.
-$$\begin{array} { l } 
y \geq 2 x - 4 \
x + 2 y \leq 7 \
x \leq 1 \
y \geq - 2
\end{array}$$

Accepted Answer

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

Question 20

Graph the system of inequalities.
-$\begin{array}{l}
4 x-y \leq-4 \
x+4 y \geq-16
\end{array}$

Accepted Answer

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

Solve. - x+5y+3z =-22 5y+4z =-30 z =-5 (3,-2,-5)

Solve. - x+y+z=7 x-y+2z=7 5x+y+z=11

Graph the system of inequalities. - 2x+y\leq4 y-1<0 $Graph the system of inequalities. - \begin{array} { l } 2 x + y \leq 4 \\ y - 1 < 0 \end{array}$

Solve the system of equations. If there is no solution to the system, give a reason. - x-6y=4 6x-5y=24

Find the solution to the system by addition (elimination) method. -2x + 10y = -56 9x + 2y = 49

Find the solution to the system by addition (elimination) method. -x + y = -6 x - y = 14

Graph the system of inequalities. - 2x+3y\geq6 x-y\leq3 y\geq2 $Graph the system of inequalities. - \begin{array} { l } 2 x + 3 y \geq 6 \\ x - y \leq 3 \\ y \geq 2 \end{array}$

If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why. -4x = 45 - 9y -2x + 7y = -11

Solve the problem. -A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 7 soft drinks for $42.00. The second group bought 7 slices of pizza and 6 soft drinks for $ 36)57. How much does one slice of pizza cost?

Find the solution to the system by addition (elimination) method. - $\frac { 1 } { 3 } x + \frac { 1 } { 3 } y = - 4$ $x - y = - 2$

Solve the system by graphing. -3x - 2y = 4 -6x + 4y = 7

Graph the system of inequalities. - $y \leq 2 x + 4$ $y > - \frac { 3 } { 4 } x$ $Graph the system of inequalities. - y \leq 2 x + 4 y > - \frac { 3 } { 4 } x$

Solve the system by graphing. -3x + y = 12 9x + 3y = 36

Find the solution to the system by addition (elimination) method. -5x + 54y = 54 3x - 6y = -6

Use the substitution method to solve the system. -x + 6y = 6 4x - 5y = -5

Solve the system by graphing. -x = -y y + x = 6

Graph the system of inequalities. - y\geq2x-4 x+2y\leq7 x\leq1 y\geq-2 $Graph the system of inequalities. - \begin{array} { l } y \geq 2 x - 4 \\ x + 2 y \leq 7 \\ x \leq 1 \\ y \geq - 2 \end{array}$

Graph the system of inequalities. - 4x-y\leq-4 x+4y\geq-16 $Graph the system of inequalities. - \begin{array}{l} 4 x-y \leq-4 \\ x+4 y \geq-16 \end{array}$

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+5y+3z =-22 5y+4z =-30 z =-5 (3,-2,-5)

Solve. - x+y+z=7 x-y+2z=7 5x+y+z=11

Graph the system of inequalities. - 2x+y\leq4 y-1<0

Solve the system of equations. If there is no solution to the system, give a reason. - x-6y=4 6x-5y=24

Find the solution to the system by addition (elimination) method. -2x + 10y = -56 9x + 2y = 49

Find the solution to the system by addition (elimination) method. -x + y = -6 x - y = 14

Graph the system of inequalities. - 2x+3y\geq6 x-y\leq3 y\geq2

If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why. -4x = 45 - 9y -2x + 7y = -11

Solve the problem. -A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 7 soft drinks for $42.00. The second group bought 7 slices of pizza and 6 soft drinks for $ 36)57. How much does one slice of pizza cost?

Find the solution to the system by addition (elimination) method. - 13x+13y=−4\frac { 1 } { 3 } x + \frac { 1 } { 3 } y = - 431​x+31​y=−4 x−y=−2x - y = - 2x−y=−2

Solve the system by graphing. -3x - 2y = 4 -6x + 4y = 7

Graph the system of inequalities. - y≤2x+4y \leq 2 x + 4y≤2x+4 y>−34xy > - \frac { 3 } { 4 } xy>−43​x

Solve the system by graphing. -3x + y = 12 9x + 3y = 36

Find the solution to the system by addition (elimination) method. -5x + 54y = 54 3x - 6y = -6

Use the substitution method to solve the system. -x + 6y = 6 4x - 5y = -5

Solve the system by graphing. -x = -y y + x = 6

Graph the system of inequalities. - y\geq2x-4 x+2y\leq7 x\leq1 y\geq-2

Graph the system of inequalities. - 4x-y\leq-4 x+4y\geq-16

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. - 2x+y\leq4 y-1<0 $Graph the system of inequalities. - \begin{array} { l } 2 x + y \leq 4 \\ y - 1 < 0 \end{array}$

Graph the system of inequalities. - 2x+3y\geq6 x-y\leq3 y\geq2 $Graph the system of inequalities. - \begin{array} { l } 2 x + 3 y \geq 6 \\ x - y \leq 3 \\ y \geq 2 \end{array}$

Find the solution to the system by addition (elimination) method. - $\frac { 1 } { 3 } x + \frac { 1 } { 3 } y = - 4$ $x - y = - 2$

Graph the system of inequalities. - $y \leq 2 x + 4$ $y > - \frac { 3 } { 4 } x$ $Graph the system of inequalities. - y \leq 2 x + 4 y > - \frac { 3 } { 4 } x$

Graph the system of inequalities. - y\geq2x-4 x+2y\leq7 x\leq1 y\geq-2 $Graph the system of inequalities. - \begin{array} { l } y \geq 2 x - 4 \\ x + 2 y \leq 7 \\ x \leq 1 \\ y \geq - 2 \end{array}$

Graph the system of inequalities. - 4x-y\leq-4 x+4y\geq-16 $Graph the system of inequalities. - \begin{array}{l} 4 x-y \leq-4 \\ x+4 y \geq-16 \end{array}$