Question 1

Determine the solution to the system of equations graphically. If the system is inconsistent or dependent, so state.
-$$\begin{array} { l } 
y = - x - 1 \
y = x - 16
\end{array}$$

Accepted Answer

A) (1, -8.5) 
B) (7.5, 8.5) 
C) (7.5, -8.5) 
D) inconsistent 
A) (1, -8.5) 
B) (7.5, 8.5) 
C) (7.5, -8.5) 
D) inconsistent C

Question 2

Solve the system using matrices.
-$$\begin{array} { l } 
3 x + 4 y = 10 \
4 x - 2 y = - 16
\end{array}$$

Accepted Answer

A) (4, -2) 
B) (-2, 4) 
C) (-2, -4) 
D) inconsistent system 
A) (4, -2) 
B) (-2, 4) 
C) (-2, -4) 
D) inconsistent system B

Question 3

Determine the solution to the system of inequalities.
-$\begin{array} { l } 
| x - 1 | \leq 2 \
x - y > 1
\end{array}$

Accepted Answer

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

Question 4

Solve the system using determinants.
-$$\begin{array} { l } 
- 2 x + 4 y - z = 19 \
x - 9 y - 5 z = - 82 \
5 x + y + z = 36
\end{array}$$

Accepted Answer

A) (5, 8, 3) 
B) (8, 3, 8) 
C) (6, 6, 3) 
D) (5, -8, -3) 
A) (5, 8, 3) 
B) (8, 3, 8) 
C) (6, 6, 3) 
D) (5, -8, -3)

Question 5

Solve the system of equations using the addition method.
-$$\begin{array} { l } 
5 x + 4 y = 61 \
5 x + 2 y = 73
\end{array}$$

Accepted Answer

A) (-17, 4) 
B) (17, -6) 
C) (-6, 17) 
D) (-17, 5) 
A) (-17, 4) 
B) (17, -6) 
C) (-6, 17) 
D) (-17, 5)

Question 6

Determine the solution to the system of inequalities.
-$\begin{array} { l } 
| x | > 2 \
y \geq - \frac { 1 } { 5 } x + 5
\end{array}$

Accepted Answer

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

Question 7

Solve the problem.
-Two cars leave a city and head in the same direction. After 7 hours, the faster car is 28 miles ahead of the slower car. The slower car has traveled 343 miles. Find the speeds of the two cars.

Accepted Answer

A) 45 mph and 49 mph 
B) 49 mph and 53 mph 
C) 40 mph and 44 mph 
D) 51 mph and 55 mph 
A) 45 mph and 49 mph 
B) 49 mph and 53 mph 
C) 40 mph and 44 mph 
D) 51 mph and 55 mph

Question 8

Find the solution to the system of equations by substitution.
-$$\begin{array} { l } 
y = - 4 x + 26 \
y = - \frac { 1 } { 2 } x + 5
\end{array}$$

Accepted Answer

A) (6, 2) 
B) (2, 6) 
C) infinite number of solutions 
D) no solution 
A) (6, 2) 
B) (2, 6) 
C) infinite number of solutions 
D) no solution

Question 9

Solve the system using determinants.
-$$\begin{array} { l } 
3 x + y + \frac { 3 } { 2 } z = - 11 \
\frac { 1 } { 2 } x + 3 z = 10 \
x 4 y = - 24
\end{array}$$

Accepted Answer

A) (-8, -4, 4) 
B) (-10, -4, 5) 
C) (-4, -5, 4) 
D) (-8, -20, 2) 
A) (-8, -4, 4) 
B) (-10, -4, 5) 
C) (-4, -5, 4) 
D) (-8, -20, 2)

Question 10

Solve the problem.
-Marcus earned $6900 during his summer vacation. He invested part of the money at 9% and the rest at 6%. If he received a total of $519 in interest at the end of the year, how much was invested at 9%?

Accepted Answer

A) $3450 
B) $1150 
C) $3500 
D) $3400 
A) $3450 
B) $1150 
C) $3500 
D) $3400

Question 11

Solve the problem.
-A twin-engined aircraft can fly 612 miles from city A to city B in 3 hours with the wind and make the return trip in 6 hours against the wind. What is the speed of the wind?

Accepted Answer

A) 51 mph 
B) 34 mph 
C) 85 mph 
D) 68 mph 
A) 51 mph 
B) 34 mph 
C) 85 mph 
D) 68 mph

Question 12

Solve the system using matrices.
-$$\begin{array} { l } 
x + y + z = - 4 \
x - y + 4 z = 19 \
2 x + 2 y + 2 z = - 9
\end{array}$$

Accepted Answer

A) (5, -4, -5) 
B) (5, -5, -4) 
C) dependent system 
D) inconsistent system 
A) (5, -4, -5) 
B) (5, -5, -4) 
C) dependent system 
D) inconsistent system

Question 13

Solve the system using matrices.
-$$\begin{array} { l } 
- 3 x - y - 2 z = - 38 \
9 x + 9 z = 117 \
2 y + z = 16
\end{array}$$

Accepted Answer

A) (-7, 5, 14) 
B) (7, 6, 5) 
C) (7, 5, 6) 
D) inconsistent 
A) (-7, 5, 14) 
B) (7, 6, 5) 
C) (7, 5, 6) 
D) inconsistent

Question 14

Determine the solution to the system of inequalities.
-$\begin{array} { l } 
| x | > 6 \
| y | \leq 5
\end{array}$

Accepted Answer

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

Question 15

Solve for the given letter.
-$$\left| \begin{array} { r r } 
- 7 & 9 \
3 & x
\end{array} \right| = - 62$$

Accepted Answer

A) 0 
B) 5 
C) 9 
D) 50 
A) 0 
B) 5 
C) 9 
D) 50

Question 16

Determine whether the ordered pair or ordered triple satisfies the system of linear equations.
-$$\begin{array} { l } 
4 x + 4 y + z = 15 \
4 x - 5 y - z = - 36 \
4 x + y + 3 z = 6 \
( - 2,5,3 )
\end{array}$$

Accepted Answer

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

Question 17

Solve the problem.
-Two planes are parallel to each other and the third plane intersects each of the other two planes as illustrated below. Is the system consistent, inconsistent, or dependent?

Accepted Answer

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

Question 18

Solve the problem.
-Mr. Alexander earns a weekly salary plus a commission from his position as a salesman. One week his total compensation on sales of $4000 was $640. The next week his total compensation on sales of $3000 was $600.
Find Mr. Alexander's weekly salary and his commission rate.

Accepted Answer

A) weekly salary: $400 
B) weekly salary: $490 commission rate: 4.8% commission rate: 3% 
C) weekly salary: $470 
D) weekly salary: $480 commission rate: 5% commission rate: 4% 
A) weekly salary: $400 
B) weekly salary: $490 commission rate: 4.8% commission rate: 3% 
C) weekly salary: $470 
D) weekly salary: $480 commission rate: 5% commission rate: 4%

Question 19

Solve the system of equations using determinants.
-$$\begin{array} { l } 
2 x - 2 y = - 2 \
2 y + 4 x = 20
\end{array}$$

Accepted Answer

A) (3, 4) 
B) (-4, 3) 
C) (4, 3) 
D) infinite number of solutions 
A) (3, 4) 
B) (-4, 3) 
C) (4, 3) 
D) infinite number of solutions

Question 20

Solve the system using matrices.
-$$\begin{array} { l } 
4 x + y = 10 \
- 4 y + 3 z = 20 \
8 x - 2 y + 3 z = 40
\end{array}$$

Accepted Answer

A) (3, -2, 5) 
B) (2, -2, 4) 
C) dependent system 
D) inconsistent system 
A) (3, -2, 5) 
B) (2, -2, 4) 
C) dependent system 
D) inconsistent system

Determine the solution to the system of equations graphically. If the system is inconsistent or dependent, so state. - y=-x-1 y=x-16

Solve the system using matrices. - 3x+4y=10 4x-2y=-16

Determine the solution to the system of inequalities. - |x-1|\leq2 x-y>1 $Determine the solution to the system of inequalities. - \begin{array} { l } | x - 1 | \leq 2 \\ x - y > 1 \end{array}$

Solve the system using determinants. - -2x+4y-z=19 x-9y-5z=-82 5x+y+z=36

Solve the system of equations using the addition method. - 5x+4y=61 5x+2y=73

Determine the solution to the system of inequalities. - |x|>2 y\geq-x+5 $Determine the solution to the system of inequalities. - \begin{array} { l } | x | > 2 \\ y \geq - \frac { 1 } { 5 } x + 5 \end{array}$

Solve the problem. -Two cars leave a city and head in the same direction. After 7 hours, the faster car is 28 miles ahead of the slower car. The slower car has traveled 343 miles. Find the speeds of the two cars.

Find the solution to the system of equations by substitution. - y=-4x+26 y=-x+5

Solve the system using determinants. - 3x+y+z=-11 x+3z=10 x4y=-24

Solve the problem. -Marcus earned $6900 during his summer vacation. He invested part of the money at 9% and the rest at 6%. If he received a total of $519 in interest at the end of the year, how much was invested at 9%?

Solve the problem. -A twin-engined aircraft can fly 612 miles from city A to city B in 3 hours with the wind and make the return trip in 6 hours against the wind. What is the speed of the wind?

Solve the system using matrices. - x+y+z=-4 x-y+4z=19 2x+2y+2z=-9

Solve the system using matrices. - -3x-y-2z=-38 9x+9z=117 2y+z=16

Determine the solution to the system of inequalities. - |x|>6 |y|\leq5 $Determine the solution to the system of inequalities. - \begin{array} { l } | x | > 6 \\ | y | \leq 5 \end{array}$

Solve for the given letter. - $\left| \begin{array} { r r } - 7 & 9 \\3 & x\end{array} \right| = - 62$

Determine whether the ordered pair or ordered triple satisfies the system of linear equations. - 4x+4y+z=15 4x-5y-z=-36 4x+y+3z=6 (-2,5,3)

Solve the problem. -Two planes are parallel to each other and the third plane intersects each of the other two planes as illustrated below. Is the system consistent, inconsistent, or dependent?

Solve the problem. -Mr. Alexander earns a weekly salary plus a commission from his position as a salesman. One week his total compensation on sales of $4000 was $640. The next week his total compensation on sales of $3000 was $600. Find Mr. Alexander's weekly salary and his commission rate.

Solve the system of equations using determinants. - 2x-2y=-2 2y+4x=20

Solve the system using matrices. - 4x+y=10 -4y+3z=20 8x-2y+3z=40

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

Filters

Exam 4: Systems of Equations and Inequalities