Question 1

Find the solution to the system of equations by substitution.
-$$\begin{array} { l } 
y = \frac { 5 } { 6 } x - \frac { 1 } { 6 } \
5 x - 6 y = - 3
\end{array}$$

Accepted Answer

A) (5, 6) 
B) (-1, -3) 
C) infinite number of solutions 
D) no solution 
A) (5, 6) 
B) (-1, -3) 
C) infinite number of solutions 
D) no solution

Question 2

Write the word or phrase that best completes each statement or answers the question.
Solve for the given letter.
-$$\left| \begin{array} { r r c } 
5 & - 3 & 1 \
- 2 & - 2 & x \
8 & 2 & - 1
\end{array} \right| = 28$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 3

Solve the system using matrices.
-$$\begin{array} { l } 
5 x - 4 y - z = - 3 \
x - 2 y - 2 z = - 24 \
- 8 x + y + z = - 48
\end{array}$$

Accepted Answer

A) (8, 7, 9) 
B) (8, 9, 7) 
C) (-8, 9, 16) 
D) inconsistent system 
A) (8, 7, 9) 
B) (8, 9, 7) 
C) (-8, 9, 16) 
D) inconsistent system

Question 4

Solve the problem.
-Three planes are parallel as illustrated below. Is the system consistent, inconsistent, or dependent?

Accepted Answer

A) consistent, not dependent 
B) consistent, dependent 
C) inconsistent 
A) consistent, not dependent 
B) consistent, dependent 
C) inconsistent

Question 5

Solve the system of equations using determinants.
-$$\begin{array} { l } 
0.8 x - 0.5 y = 0.9 \
0.7 x + 0.4 y = - 3.4
\end{array}$$

Accepted Answer

A) (-2, -5) 
B) (-1.5, 1) 
C) (-1.5, -4.2) 
D) (-2, 1) 
A) (-2, -5) 
B) (-1.5, 1) 
C) (-1.5, -4.2) 
D) (-2, 1)

Question 6

Determine the solution to the system of equations graphically. If the system is inconsistent or dependent, so state.
-$$\begin{array} { c } 
4 x - 5 y = 4 \
15 y = 12 x - 8
\end{array}$$

Accepted Answer

A) (4, 4) 
B)  $\left( 2 , - \frac { 5 } { 2 } \right)$ 
C) dependent 
D) inconsistent 
A) (4, 4) 
B)  $\left( 2 , - \frac { 5 } { 2 } \right)$ 
C) dependent 
D) inconsistent

Question 7

Determine whether the ordered pair or ordered triple satisfies the system of linear equations.
-$$\begin{array} { l } 
4 x + 2 y + z = - 14 \
2 x - 2 y - z = 8 \
5 x + y + 5 z = - 28 \
( - 4 , - 3 , - 1 )
\end{array}$$

Accepted Answer

A) solution 
B) not a solution 
A) solution 
B) not a solution

Question 8

Solve the system of equations using the addition method.
-$$\begin{array} { l } 
- 3 x - 2 y = 4 \
- 6 y = 12 + 9 x
\end{array}$$

Accepted Answer

A) (-3, -2) 
B) (0, 0) 
C) infinite number of solutions 
D) no solution 
A) (-3, -2) 
B) (0, 0) 
C) infinite number of solutions 
D) no solution

Question 9

Solve the system of equations using determinants.
-$$\begin{array} { l } 
6 x + 5 y = - 15 \
5 x + y = - 22
\end{array}$$

Accepted Answer

A) (3, -5) 
B) (-5, 3) 
C) (-3, -5) 
D) no solution 
A) (3, -5) 
B) (-5, 3) 
C) (-3, -5) 
D) no solution

Question 10

Evaluate the determinant.
-$$\left| \begin{array} { l l } 
- 6 & 5 \
- 2 & 2
\end{array} \right|$$

Accepted Answer

A) -2 
B) -26 
C) -22 
D) 2 
A) -2 
B) -26 
C) -22 
D) 2

Question 11

Solve the system using determinants.
-$$\begin{array} { l } 
3 x + y - 3 z = 6 \
- x + 3 y + 2 z = 6 \
- 5 x - 5 x + 4 z = - 18
\end{array}$$

Accepted Answer

A) (-3, 3, -3) 
B) (0, 0, -2) 
C) infinite number of solutions 
D) no solution 
A) (-3, 3, -3) 
B) (0, 0, -2) 
C) infinite number of solutions 
D) no solution

Question 12

Evaluate the determinant.
-$$\left| \begin{array} { l l } 
9 & 2 \
4 & 7
\end{array} \right|$$

Accepted Answer

A) 55 
B) -55 
C) 71 
D) -10 
A) 55 
B) -55 
C) 71 
D) -10

Question 13

Determine whether the system is inconsistent, dependent, or neither.
-$$\begin{array} { l } 
x + y + z = - 5 \
x - y + 3 z = - 15 \
5 x + 5 y + 5 z = - 13
\end{array}$$

Accepted Answer

A) dependent 
B) inconsistent 
C) neither 
A) dependent 
B) inconsistent 
C) neither

Question 14

Determine whether the ordered pair or ordered triple satisfies the system of linear equations.
-$$\begin{array} { l } 
y = - x - 1 \
x - y = - 7 \
( 4,3 )
\end{array}$$

Accepted Answer

A) solution 
B) not a solution 
A) solution 
B) not a solution

Question 15

Solve the problem.
-Three planes intersect as illustrated below. Is the system consistent, inconsistent, or dependent?

Accepted Answer

A) inconsistent 
B) consistent, dependent 
C) consistent, not dependent 
A) inconsistent 
B) consistent, dependent 
C) consistent, not dependent

Question 16

Evaluate the determinant.
-$$\left| \begin{array} { c c } 
\frac { 1 } { 5 } & - \frac { 1 } { 10 } \
10 & 5
\end{array} \right|$$

Accepted Answer

A) -2 
B) 0 
C) 2 
D)  $\frac { 5 } { 2 }$ 
A) -2 
B) 0 
C) 2 
D)  $\frac { 5 } { 2 }$

Question 17

Solve the system of equations using the addition method.
-$$\begin{array} { l } 
4 x + y + \frac { 3 } { 2 } z = 14 \
\frac { 3 } { 2 } x + 3 z = - 3 \
x + 4 y = - 10
\end{array}$$

Accepted Answer

A) (6, -4, -4) 
B) (2, -23, -6) 
C) (2, -3, -4) 
D) (-2, -3, -1) 
A) (6, -4, -4) 
B) (2, -23, -6) 
C) (2, -3, -4) 
D) (-2, -3, -1)

Question 18

Solve the system using matrices.
-$$\begin{array} { l } 
5 x + 4 y = 32 \
- 9 x + 7 y = - 86
\end{array}$$

Accepted Answer

A) (7, -1) 
B) (8, -2) 
C) (-8, -1) 
D) inconsistent system 
A) (7, -1) 
B) (8, -2) 
C) (-8, -1) 
D) inconsistent system

Question 19

Solve the system using determinants.
-$$\begin{array} { l } 
- 0.1 x + 0.3 y - 0.4 z = - 2.1 \
- 0.3 x - 0.1 y + 0.2 z = 0.3 \
0.2 x - 0.4 y - 0.1 z = 0.4
\end{array}$$

Accepted Answer

A) (-0.3, -6, 4) 
B) (-0.2, -6, 5) 
C) (-0.3, -3, 5) 
D) (2, -1, 4) 
A) (-0.3, -6, 4) 
B) (-0.2, -6, 5) 
C) (-0.3, -3, 5) 
D) (2, -1, 4)

Question 20

Find the solution to the system of equations by substitution.
-$$\begin{array} { l } 
x + 4 y = 7 \
- 3 x - 12 y = - 21
\end{array}$$

Accepted Answer

A) (7, 0) 
B) (0, 0) 
C) infinite number of solutions 
D) no solution 
A) (7, 0) 
B) (0, 0) 
C) infinite number of solutions 
D) no solution

Find the solution to the system of equations by substitution. - y=x- 5x-6y=-3

Write the word or phrase that best completes each statement or answers the question. Solve for the given letter. - $\left| \begin{array} { r r c } 5 & - 3 & 1 \\- 2 & - 2 & x \\8 & 2 & - 1\end{array} \right| = 28$

Solve the system using matrices. - 5x-4y-z=-3 x-2y-2z=-24 -8x+y+z=-48

Solve the problem. -Three planes are parallel as illustrated below. Is the system consistent, inconsistent, or dependent?

Solve the system of equations using determinants. - 0.8x-0.5y=0.9 0.7x+0.4y=-3.4

Determine the solution to the system of equations graphically. If the system is inconsistent or dependent, so state. - 4x-5y=4 15y=12x-8

Determine whether the ordered pair or ordered triple satisfies the system of linear equations. - 4x+2y+z=-14 2x-2y-z=8 5x+y+5z=-28 (-4,-3,-1)

Solve the system of equations using the addition method. - -3x-2y=4 -6y=12+9x

Solve the system of equations using determinants. - 6x+5y=-15 5x+y=-22

Evaluate the determinant. - $\left| \begin{array} { l l } - 6 & 5 \\- 2 & 2\end{array} \right|$

Solve the system using determinants. - 3x+y-3z=6 -x+3y+2z=6 -5x-5x+4z=-18

Evaluate the determinant. - $\left| \begin{array} { l l } 9 & 2 \\4 & 7\end{array} \right|$

Determine whether the system is inconsistent, dependent, or neither. - x+y+z=-5 x-y+3z=-15 5x+5y+5z=-13

Determine whether the ordered pair or ordered triple satisfies the system of linear equations. - y=-x-1 x-y=-7 (4,3)

Solve the problem. -Three planes intersect as illustrated below. Is the system consistent, inconsistent, or dependent?

Evaluate the determinant. - $\left| \begin{array} { c c } \frac { 1 } { 5 } & - \frac { 1 } { 10 } \\10 & 5\end{array} \right|$

Solve the system of equations using the addition method. - 4x+y+z=14 x+3z=-3 x+4y=-10

Solve the system using matrices. - 5x+4y=32 -9x+7y=-86

Solve the system using determinants. - -0.1x+0.3y-0.4z=-2.1 -0.3x-0.1y+0.2z=0.3 0.2x-0.4y-0.1z=0.4

Find the solution to the system of equations by substitution. - x+4y=7 -3x-12y=-21

Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

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Exam 4: Systems of Equations and Inequalities