Deck 3: Systems of Equations

Question 1

Use the graphs in the illustration to solve the equation. $- 3 x + 9 = x + 1$

A) x=3
B) x=4
C) x=2
D) x=-4
E) x=-2

Answer 1

x=2

Question 2

Solve the following system of equations by graphing, if possible. Then write the solution as an ordered pair. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { r } 2 x + 3 y = 9 \\x = 3\end{array} \right.$

A) (1,3)
B) (3,1)
C) inconsistent
D) dependent

Answer 2

(3,1)

Question 3

Solve the system by graphing. $\left\{ \begin{array} { l } 2 x + y = 0 \\x - 2 y = - 15\end{array} \right.$

A)
B)
C)
D)
E)

Answer 3

Question 4

Tell whether the ordered pair (4,-5) is a solution of the system of equations. $\left\{ \begin{array} { l } y + 4 = \frac { 1 } { 4 } x \\5 x + 4 y = 0\end{array} \right.$

A) no
B) yes

Question 5

Two airplanes, flying at the same altitude, are tracked using the same coordinate system on a radar screen. One plane is following a path described by the equation $y = \frac { 2 } { 3 } x - 4$ , and the other is following a path described by the equation $2 x = 3 y + 9$ . Is there a possibility of a collision?

A) yes
B) no

Question 6

Use the graphs in the illustration to solve the equation. $- x - 4 = 2 x - 1$

A) x=1
B) x=-1
C) x=2
D) x=-2
E) x=3

Question 7

Solve the system by graphing. $\left\{ \begin{array} { l } 2 x + y = 2 \\x + y = 0\end{array} \right.$

A)
B)
C)
D)
E)

Question 8

Tell whether the ordered pair (3,3) is a solution of the system of equations. $\left\{ \begin{array} { l } 5 x - y = 12 \\y = \frac { 1 } { 2 } x + \frac { 3 } { 2 }\end{array} \right.$

A) yes
B) no

Question 9

Solve the system by graphing. $\left\{ \begin{array} { l } y = - 4 \\y = \frac { 13 } { 4 } x - \frac { 3 } { 4 }\end{array} \right.$

A)
B)
C)
D)
E)

Question 10

Solve the system by graphing. $\left\{ \begin{array} { l } 4 x = 4 - 3 y \\4 x + 3 y = 7\end{array} \right.$

A)
B)
C)
D)
E)

Question 11

Solve the system by graphing. $\left\{ \begin{array} { l } y = 4 \\x = 5\end{array} \right.$

A)
B)
C)
D)
E)

Question 12

Which of the following ordered pairs is a solution of the system $\left\{ \begin{array} { l } 4 x - 6 y = 15 \\8 x + 2 y = 2\end{array} \right.$ .

A) $\left( 2 , - \frac { 1 } { 2 } \right)$
B) $\left( 0 , - \frac { 7 } { 3 } \right)$
C) $\left( \frac { 3 } { 4 } , - 2 \right)$
D) $( 1,3 )$

Question 13

Solve the system by graphing. $\left\{ \begin{array} { l } x = 2 \\y = - \frac { 1 } { 2 } x + 3\end{array} \right.$

A)
B)
C)
D)
E)

Question 14

Refer to the illustration. Answer the questions. How many solutions does the system of equations have? Are the equations dependent or independent?

A) no solution, independent equations
B) no solution, dependent equations
C) infinite number of solutions, dependent equations
D) two solutions, independent equations
E) one solution, independent equations

Question 15

Determine if $\left( 4 , - \frac { 1 } { 3 } \right)$ is a solution of the system $\left\{ \begin{array} { l } 5 x - 3 y = 21 \\\frac { 1 } { 2 } x - 3 y = 3\end{array} \right.$

A) not a solution
B) solution

Question 16

Solve the system by graphing. $\left\{ \begin{array} { l } x + y = 0 \\y = 2 x - 9\end{array} \right.$

A)
B)
C)
D)
E)

Question 17

Determine whether the ordered pair $\left( \frac { 1 } { 3 } , \frac { 1 } { 2 } \right)$ is a solution of the following system. $\left\{ \begin{array} { c } 6 x - 8 y = - 2 \\- 6 x + 10 y = 3\end{array} \right.$

A) not a solution
B) solution

Question 18

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

A)
B)
C)
D)
E)

Question 19

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

A)
B)
C)
D)
E)

Question 20

Refer to the illustration.
(a) How many ordered pairs satisfy the equation $5 x + y = 5$ ?
(b) How many ordered pairs satisfy the equation $\frac { 3 } { 4 } x - y = - 5$ ?
(c) How many ordered pairs satisfy both equations?

A) (a) infinitely many (b) infinitely many (c) infinitely many
B) (a) infinitely many (b) infinitely many (c) one
C) (a) one (b) one (c) infinitely many
D) (a) one (b) one (c) one
E) (a) infinitely many (b) infinitely many (c) none

Question 21

When a system of equations has at least one solution, it is called a(n) __________ system. If a system has no solutions, it is called a(n) __________ system.

Question 22

Tell whether the ordered pair is a solution of the system of equations.

Question 23

Two airplanes, flying at the same altitude, are tracked using the same coordinate system on a radar screen. One plane is following a path described by the equation , and the other is following a path described by the equation . Is there a possibility of a collision?

Question 24

When solving a system of two linear equations by the graphing method, we look for the point of __________ of the two lines.

Question 25

Tell whether the ordered pair is a solution of the system of equations.

Question 26

Refer to the illustration. How many ordered pairs satisfy the equation ?
__________ Complete the pairs, if they are known to satisfy the equation . How many ordered pairs satisfy the equation ?
__________ Complete the pairs, if they are known to satisfy the equation . How many ordered pairs satisfy both equations?
__________ Name the pair(s). __________

Question 27

If two lines are parallel,

A) the equations are independent and the system is inconsistent.
B) the equations are independent and the system is consistent.
C) the equations are dependent.
D) none of these.

Question 28

Consider the system . In order for this system to be inconsistent, what does the value of B need to be?

Question 29

Solve the following system by graphing. Write the solution as an ordered pair. If a system is inconsistent or is the equations are independent, so state.

Question 30

Refer to the illustration. Answer the questions. How many solutions does the system of equations have?
__________ Are the equations dependent or independent?
__________

Question 31

Solve $\left\{ \begin{array} { l } x + y = 1 \\x - y = 3\end{array} \right.$

A) No solution
B) Solution: (-1,2)
C) Solution: (2,-1)
D) Solution: $( 2 , - 1 )$

Question 32

If two equations have different graphs, they are called __________ equations. Two equations with the same graph are called __________ equations.

Question 33

is called a(n) __________ of equations.

Question 34

Refer to the illustration. Decide whether a true or a false statement would be obtained when the coordinates of Point are substituted into the equation for line . __________ Point are substituted into the equation for line . __________ Point are substituted into the equation for line . __________ Point are substituted into the equation for line .__________

Question 35

Consider the system . In order for the equations to be dependent, what does the value of A need to be?

Question 36

Use the graphs in the illustration to solve the equation. __________

Question 37

Use the graphs in the illustration to solve the equation. __________

Question 38

Without graphing, how can you tell that the graphs of do no intersect?

Question 39

Without graphing, how can you tell that the graphs of intersect?

Question 40

Solve the following system of equations by graphing, if possible. Then write the solution as an ordered pair. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } 2 y - x = - 4 \\y = \frac { 1 } { 2 } x - 2\end{array} \right.$

A) infinitely many solutions;dependent equations
B) no solution; inconsistent system
C) (-6, 4)
D) $1$

Question 41

Solve the system by any method, if possible. $\sqrt { - 2 } \sqrt { - 14 }$

A) $7 \sqrt { 2 } i$
B) $2 \sqrt { 7 } i$
C) $- 2 \sqrt { 7 }$
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 42

Solve the system. To do so, substitute $a + b i$ for $- 3 i ( 6 - 6 i )$ and $- 10 - 10 i$ for $14 - 14 i$ and solve for $16 - 16 i$ and $- 12 + 12 i$ . Then find $- 18 - 18 i$ and $- 3$ using the fact that and . $\varnothing$

A)
B) $( 5,6 )$
C) $( - 5,6 )$
D) $( - 5 , - 6 )$
E) $( - 6 , - 5 )$

Question 43

Solve the system by any method, if possible. $x ^ { 2 } - 2 x = 7$

A) $x = 1 \pm 2 \sqrt { 2 }$
B) $16 i$
C) $- 36 i$
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 44

Solve the system by elimination if possible. $\log _ { 6 } x + \log _ { 6 } ( x - 20 ) = \log _ { 6 } 189$

A) $\left\{ \frac { 209 } { 2 } \right\}$
B) $\log _ { 5 } \frac { ( x - 2 ) ^ { 5 } } { x }$
C) $\log _ { 5 } x ( x - 2 ) ^ { 5 }$
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 45

Solve the system by elimination if possible. $\log _ { 3 } ( x - 5 ) + \log _ { 3 } ( x + 3 ) = \log _ { 3 } 20$

A) (3, 7)
B) $8 \log x - \log y$
C) (7, 3)
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 46

Solve the system by substitution, if possible. $5 ^ { x } = 9$

A) $- 0.5579$
B) $- 1.7925$
C) $v ^ { - 3 }$
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 47

Solve the system by any method, if possible. ${ } ^ { 227 } \mathrm { Th }$

A) $y = - \frac { 21 } { 11 }$
B) $\log _ { 3 } 36$
C) $- 0.3021$
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 48

Solve the system using the substitution method, if possible. $\log ( x + 5 ) - \log ( x - 2 ) = \log 6$

A) $\left\{ \frac { 17 } { 5 } \right\}$
B) $\left\{ \frac { 9 } { 5 } \right\}$
C) $\{ - 3 \}$
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 49

Solve the system by any method, if possible. $\log _ { 7 } \frac { x y } { 7 }$

A) $\log _ { 7 } x + \log _ { 7 } y - 1$
B) $\log _ { 7 } x - \log _ { 7 } y + 1$
C) $7 \log _ { 7 } x + \log _ { 7 } y$
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 50

Solve the system by elimination if possible. $3 ^ { 3 x - 3 } = 729$

A) (1, 6)
B) $\left\{ \frac { 7 } { 2 } \right\}$
C) (6, 1)
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 51

Solve the system by substitution, if possible. $\log x + \log ( x - 15 ) = 2$

A) (8, 3)
B) $\left\{ \frac { 500 } { 33 } \right\}$
C) (3, 8)
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 52

In solving a system of equations by the elimination method, the result 7 = 7 is obtained. Which of the following statements is true?

A) The system is consistent.
B) The system is inconsistent.
C) The equations are dependent.
D) There is only one solution.

Question 53

The system of equations $a + b i$ will be solved by substitution. If substituting the expression for y in equation 1 into equation 2, the new equation is

A) -17 x - 24 = 4
B) 28 x + 24 = 4
C) 4 x - 8 = 4
D) 28 x - 24 = 4

Question 54

Solve the system by any method if possible. $\log _ { 5 } 3$

A) $\frac { \log 3 } { \log 5 }$
B) $\frac { \log 5 } { \log 3 }$
C) $\frac { \ln 5 } { \ln 3 }$
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 55

Elimination will be used to solve the system $a + b i$ . Which of the following equations is equivalent to equation 1 and can be added to equation 2 to eliminate y ?

A) -24 x + 4 y = 28
B) 24 x + 4 y = $\frac { 65 } { 8 - i }$ 7
C) 24 x + 4 y = $4 - 7 i$ 28
D) none of these

Question 56

Use the method of substitution to find the x -coordinate of the solution of the following system of equations. $a + b i$

A) $( 5 - 2 i ) ( 2 + 5 i )$
B) $12 + 5 i$
C) $16 + 21 i$
D) $14 - 2 i$

Question 57

Solve the system by any method, if possible. Give your answer in the form of ( m, n) . $\log _ { 5 } 9$

A) $\log _ { b } 7 = 0.8451$
B) $\log _ { b } 9 = 0.9542$
C) $\log _ { b } 63$
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 58

Use the method of elimination to find the y -coordinate of the solution of the following system of equations. $i ^ { 28 }$

A) $1$
B) $- i$
C) $\sqrt { i }$
D) $- 1$

Question 59

Solve the following system of equations by any method. $( 5 + \sqrt { - 4 } ) - ( 7 - \sqrt { - 25 } )$

A) $- 2 + 7 i$
B) no solution; inconsistent system
C) infinitely many solutions; dependent equations
D) $- 2 - 3 i$

Question 60

Solve the system by any method, if possible. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

A) $1 + \log _ { 4 } 9 x - \log _ { 4 } y$
B) $1 + 9 \log _ { 4 } x - \log _ { 4 } y$
C) $\log _ { 4 } 36 + \log _ { 4 } x - \log _ { 4 } y$
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question 61

Solve the system by any method, if possible. If the system is inconsistent or if the equations are dependent, so indicate.

Question 62

Solve the system by any method, if possible. If the system is inconsistent, or if the equations are dependent, so indicate.

Question 63

Solve the system by substitution, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Question 64

Solve the following system of equations by elimination. $a + b i$

A) $( 4 + 2 i ) ( 1 - 9 i )$
B) (4, 6)
C) infinitely many solutions; dependent equations
D) no solution; inconsistent system

Question 65

Find the x -coordinate of the solution of the following system. Use the method of elimination. $( - 5 + 3 i ) - ( 3 - i )$

A) $- 8 + 2 i$
B) $2 + 2 i$
C) $- 2 + 4 i$
D) $- 8 + 4 i$

Question 66

Find the y -coordinate of the solution of the following system. Use the method of substitution. $- \sqrt { - 36 }$

A) $6$
B) $- 6$
C) $6 i$
D) $- 6 i$

Question 67

A student is solving the system $10$ by elimination. Which of the following systems is the result if the student wants to eliminate y ?

A) $- 1$
B) $1$
C) $- i$
D) $i$

Question 68

Solve the system by elimination if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Question 69

Solve the system by elimination if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Question 70

Solve the system by any method if possible. If the system is inconsistent or if the equations are dependent, so indicate.

Question 71

Solve the system by elimination if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Question 72

Find the value of b that makes the following system inconsistent. $\sqrt { - 4 } \cdot \sqrt { - 100 }$

A) b = 36
B) b = - 36
C) $20 i$
D) $20$

Question 73

Solve the system using the substitution method, if possible. If the system is inconsistent or if the equations are dependent , so indicate.

Question 74

When we add the two equations of the system , the y -terms are __________.

Question 75

Solve the system by substitution, if possible. If the system is inconsistent or if the equations are dependent, so indicate.

Question 76

Solve the system by any method, if possible. If the system is inconsistent or if the equations are dependent, so indicate.

Question 77

Solve the system. To do so, substitute for and for and solve for and . Then find and using the fact that and .

Question 78

Solve the system by any method, if possible. If the system is inconsistent, or if the equations are dependent, so indicate.

Question 79

is the __________ form of a linear equation.

Question 80

To solve , we can __________ for y in the second equation.