Deck 9: Systems of Linear Equations

Question 1

Solve the pair of linear equations by addition. $\begin{array} { r } x + y = 13 \\x - y = 3\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 8,5 )$
B) $( 9,4 )$
C) $( 9 , - 5 )$
D) The lines are parallel.
E) The lines coincide.

Answer 1

$( 9 , - 5 )$

Question 2

Solve the pair of linear equations by addition. $\begin{array} { c } 2 x + 8 y = 8 \\4 x + 16 y = 5\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 0,2 )$
B) $( 9,0 )$
C) $( 6,2 )$
D) The lines are parallel.
E) The lines coincide.

Answer 2

The lines are parallel.

Question 3

Solve the pair of linear equations by addition. $\begin{array} { l } 2 x - 3 y = 13 \\3 x + 5 y = 10\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 5 , - 1 )$
B) $( - 6 , - 1 )$
C) $( 6,4 )$
D) The lines are parallel.
E) The lines coincide.

Answer 3

$( 5 , - 1 )$

Question 4

Solve the pair of linear equations by addition. $\begin{array} { c } 2 x + 3 y = - 6 \\2 x - y = 18\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 6 , - 4 )$
B) $( 6 , - 6 )$
C) $( 5,6 )$
D) The lines are parallel.
E) The lines coincide.

Question 5

Solve the pair of linear equations by addition. $\begin{array} { l } 4 x + 14 y = 42 \\8 x + 17 y = 51\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( - 4 , - 5 )$
B) $( 0 , - 3 )$
C) $( 0,3 )$
D) The lines are parallel.
E) The lines coincide.

Question 6

Solve the pair of linear equations by addition. $\begin{array} { r } 7 x - 2 y = 23 \\9 x + y = 31\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $\left( 5 , \frac { 2 } { 5 } \right)$
B) $\left( 5 \frac { 2 } { 5 } , 2 \right)$
C) $\left( 3 \frac { 2 } { 5 } , \frac { 2 } { 5 } \right)$
D) The lines are parallel.
E) The lines coincide.

Question 7

Solve the pair of linear equations by addition. $\begin{array} { l } 7 x - 4 y = 16 \\3 x - 2 y = 8\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 9 , - 4 )$
B) $( 0,5 )$
C) $( 0 , - 4 )$
D) The lines are parallel.
E) The lines coincide.

Question 8

Solve the pair of linear equations by addition. $\begin{array} { l } 3 x - 3 y = 4 \\4 x - 3 y = 0\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $\left( - 1 , - \frac { 1 } { 3 } \right)$
B) $\left( - 4 , - 5 \frac { 1 } { 3 } \right)$
C) $\left( - \frac { 1 } { 4 } , - 5 \frac { 1 } { 3 } \right)$
D) The lines are parallel.
E) The lines coincide.

Question 9

Solve the pair of linear equations by addition. $\begin{array} { l } 3 x + 2 y = 14 \\x + 8 y = - 32\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 8,3 )$
B) $( 8 , - 5 )$
C) $( 9 , - 5 )$
D) The lines are parallel.
E) The lines coincide.

Question 10

Solve the pair of linear equations by addition. $\begin{array} { l } \frac { 1 } { 5 } x - \frac { 2 } { 7 } y = 1 \\2 x - 2 y = 7\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $\left( \frac { 1 } { 2 } , - \frac { 1 } { 2 } \right)$
B) $\left( 0 , - \frac { 1 } { 2 } \right)$
C) $\left( 0 , - 3 \frac { 1 } { 2 } \right)$
D) The lines are parallel.
E) The lines coincide.

Question 11

Solve the pair of linear equations by addition. $\begin{array} { c } 4 x - 3 y = 8 \\8 x - 6 y = 16\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 4 , - 7 )$
B) $( - 9,7 )$
C) $( 9,2 )$
D) The lines are parallel.
E) The lines coincide.

Question 12

Solve the pair of linear equations by addition. $\begin{array} { l } - 3 x + 2 y = 8 \\- 4 x - 2 y = 6\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( - 2,1 )$
B) $( 3,1 )$
C) $( 2 , - 1 )$
D) The lines are parallel.
E) The lines coincide.

Question 13

Solve the pair of linear equations by addition. $\begin{array} { l } 5 x - 2 y = - 10 \\2 x + 4 y = - 4\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 0 , - 1 )$
B) $( - 6 , - 4 )$
C) $( - 2,0 )$
D) The lines are parallel.
E) The lines coincide.

Question 14

Solve the pair of linear equations by addition. $\begin{array} { l } 12 x + 16 y = 72 \\4 x - 12 y = 128\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 12,7 )$
B) $( 14 , - 6 )$
C) $( - 12,6 )$
D) The lines are parallel.
E) The lines coincide.

Question 15

Solve the pair of linear equations by addition. $\begin{array} { l } 9 x + 6 y = 0 \\6 x - 3 y = 63\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 6 , - 7 )$
B) $( 6 , - 9 )$
C) $( 5,9 )$
D) The lines are parallel.
E) The lines coincide.

Question 16

Solve the pair of linear equations by addition. $\begin{array} { l } 15 x + 4 y = 29 \\16 x + 5 y = 28\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 3 , - 4 )$
B) $( 4,5 )$
C) $( 4 , - 4 )$
D) The lines are parallel.
E) The lines coincide.

Question 17

Solve the pair of linear equations by addition. $\begin{array} { l } 9 x - 5 y = - 45 \\3 x - 17 y = - 15\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( - 5,0 )$
B) $( 6,7 )$
C) $( 6,0 )$
D) The lines are parallel.
E) The lines coincide.

Question 18

Solve the pair of linear equations by addition. $\begin{array} { l } 3 x - 2 y = 18 \\3 x + 4 y = 26\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $\left( 6 \frac { 8 } { 9 } , 1 \frac { 1 } { 3 } \right)$
B) $\left( 4 , - 1 \frac { 1 } { 3 } \right)$
C) $\left( 3 \frac { 8 } { 9 } , 4 \frac { 1 } { 3 } \right)$
D) The lines are parallel.
E) The lines coincide.

Question 19

Solve the pair of linear equations by addition. $\begin{array} { l } 6 x + 9 y = 6 \\9 x - 6 y = 9\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 1,0 )$
B) $( 7,5 )$
C) $( 0,5 )$
D) The lines are parallel.
E) The lines coincide.

Question 20

Solve the pair of linear equations by addition. $\begin{array} { c } 2 x - y = 2 \\3 x + y = 3\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.

A) $( 2,0 )$
B) $( 2 , - 2 )$
C) $( 1,0 )$
D) The lines are parallel.
E) The lines coincide.

Question 21

Solve the pair of linear equations by addition. $\begin{array} { l } 7 x - 8 y = - 7 \\3 x - 19 y = - 3\end{array}$

Question 22

Solve the pair of linear equations by addition. $\begin{array} { l } 7 x - 6 y = 18 \\5 x - 6 y = 18\end{array}$

Question 23

Solve the pair of linear equations by addition. $\begin{array} { l } 2 x - 5 y = 22 \\5 x + 9 y = 12\end{array}$

Question 24

Solve the pair of linear equations by addition. $\begin{array} { c } 9 x - 6 y = 27 \\6 x + y = 21\end{array}$

Question 25

Solve the pair of linear equations by addition. $\begin{array} { l } 5 x + 2 y = 0 \\2 x - 5 y = 29\end{array}$

Question 26

Solve the pair of linear equations by addition. $\begin{array} { c } x + y = 11 \\x - y = 1\end{array}$

Question 27

Solve the pair of linear equations by addition.
  $\begin{array} { c } 6 x - 5 y = 7 \\12 x - 10 y = 14\end{array}$

Question 28

Solve the pair of linear equations by addition. $\begin{array} { c } - 4 x + 2 y = 10 \\- 3 x - 2 y = 4\end{array}$

Question 29

Solve the pair of linear equations by addition. $\begin{array} { l } \frac { 1 } { 5 } x - \frac { 2 } { 9 } y = 1 \\5 x - 8 y = 36\end{array}$

Question 30

Solve the pair of linear equations by addition.
  $\begin{array} { l } 5 x - 2 y = - 15 \\2 x + 4 y = - 6\end{array}$

Question 31

Solve the pair of linear equations by addition. $\begin{array} { l } 14 x + 16 y = 100 \\4 x - 14 y = 140\end{array}$

Question 32

Solve the pair of linear equations by addition. $\begin{array} { l } 2 x - 2 y = 3 \\3 x - 2 y = 0\end{array}$

Question 33

Solve the pair of linear equations by addition. $\begin{array} { l } 12 x + 9 y = 12 \\13 x + 10 y = 12\end{array}$

Question 34

Solve the pair of linear equations by addition. $\begin{array} { l } 3 x - 2 y = 20 \\3 x + 4 y = 30\end{array}$

Question 35

Solve the pair of linear equations by addition. $\begin{array} { l } 4 x + 13 y = 52 \\8 x + 15 y = 60\end{array}$

Question 36

Solve the pair of linear equations by addition. $\begin{array} { c } 3 x + 4 y = - 3 \\3 x - y = 27\end{array}$

Question 37

Solve the pair of linear equations by addition. $\begin{array} { c } 5 x + 9 y = 9 \\15 x + 27 y = 4\end{array}$

Question 38

Solve the pair of linear equations by addition. $\begin{array} { l } 4 x + 9 y = 12 \\9 x - 4 y = 27\end{array}$

Question 39

Solve the pair of linear equations by addition. $\begin{array} { l } 4 x + 2 y = 24 \\x + 7 y = - 7\end{array}$

Question 40

Solve the pair of linear equations by addition. $\begin{array} { c } 3 x - y = 5 \\2 x + y = 10\end{array}$

Question 41

Solve, using the substitution method, and check. $\begin{array} { l } 5 x - 4 y = 3 \\2 x + y = 22\end{array}$

A) (7, -8)
B) (2, 13)
C) (8, 9)
D) (4, 11)
E) (7, 8)

Question 42

Solve, using the substitution method, and check. $\begin{array} { c } 3 x + 8 y = 80 \\y = 2 x - 9\end{array}$

A) (13, 12)
B) (8, -7)
C) (11, 4)
D) (8, 7)
E) (7, 6)

Question 43

Solve, using the substitution method, and check. $\begin{array} { l } x + 6 y = - 26 \\5 x - 8 y = - 16\end{array}$

A) (-8, -3)
B) (13, 8)
C) (5, 6)
D) (8, 3)
E) (-9, -2)

Question 44

Solve, using the substitution method, and check. $\begin{array} { c } 2 x + 4 y = - 14 \\x = 3 y\end{array}$

A) (8.4, 2.8)
B) (-4.2, -1.4)
C) (-4.8, -1.6)
D) (-8.4, -1.4)
E) (2.4, 0.8)

Question 45

Solve, using the substitution method, and check. $\begin{array} { c } 2 x + 3 y = 4 \\5 x - 6 y = - 71\end{array}$

A) (2, -11)
B) (-6, 5)
C) (4, -3)
D) (7, 6)
E) (-7, 6)

Question 46

Solve, using the substitution method, and check. $\begin{array} { l } 4 x - 5 y = 7 \\x = 18 - 2 \mathrm { y }\end{array}$

A) (13, 10)
B) (8, 5)
C) (11, 2)
D) (-8, 5)
E) (7, 6)

Question 47

Solve, using the substitution method, and check. $\begin{array} { c } 9 x - y = 11 \\y = - x\end{array}$

A) $\left( - \frac { 11 } { 10 } , \frac { 11 } { 10 } \right)$
B) $\left( \frac { 11 } { 10 } , - \frac { 11 } { 10 } \right)$
C) $\left( - \frac { 10 } { 11 } , \frac { 10 } { 11 } \right)$
D) $\left( \frac { 10 } { 11 } , - \frac { 10 } { 11 } \right)$
E) $\left( - \frac { 11 } { 10 } , - \frac { 11 } { 10 } \right)$

Question 48

Solve, using the substitution method, and check. $\begin{array} { c } 3 x + y = 6 \\y = 2 x\end{array}$

A) (2.2, 4.4)
B) (3.8, 7.6)
C) (6, 12)
D) (1.2, 2.4)
E) (3, 6)

Question 49

Solve, using the substitution method, and check. $\begin{array} { l } 3 x + 4 y = 43 \\x - 5 y = - 30\end{array}$

A) (2, 4)
B) (4, 6)
C) (5, 7)
D) (10, 2)
E) (-5, -7)

Question 50

Solve, using the substitution method, and check. $\begin{array} { c } 7 x + 8 y + 124 = 0 \\y = 3 x\end{array}$

A) (7, 15)
B) (-4, -12)
C) (9, 7)
D) (4, -12)
E) (-3, -9)

Question 51

Solve, using the substitution method, and check. $\begin{array} { c } 6 x - 8 y = 299 \\x = - \frac { y } { 5 }\end{array}$

A) (9.5, -35.5)
B) (4, -20)
C) (7.5, -37.5)
D) (6.5, -32.5)
E) (6.5, 32.5)

Question 52

Solve, using the substitution method, and check. $\begin{array} { l } 8 y - 2 x = - 78 \\x = - 25 - 4 y\end{array}$

A) (12, -13)
B) (7, -8)
C) (6, -9)
D) (7, 8)
E) (4, -11)

Question 53

Solve, using the substitution method, and check. $\begin{array} { c } 4 x + 5 y = 70 \\4 x = - 15 y\end{array}$

A) (25.25, -6)
B) (26.25, -7)
C) (8, -8)
D) (31.25, -2)
E) (23.25, -10)

Question 54

Solve, using the substitution method, and check. $\begin{array} { c } 2 y + 7 x = 68 \\y = 3 x - 18\end{array}$

A) (-8, -6)
B) (8, 6)
C) (13, 1)
D) (9, 5)
E) (11, 3)

Question 55

Solve, using the substitution method, and check. $\begin{array} { l } 3 x + 4 y = 25 \\- 5 x + 2 y = - 7\end{array}$

A) (6, 1)
B) (-3, 4)
C) (3, 4)
D) (2, 5)
E) (8, 9)

Question 56

Solve, using the substitution method, and check. $\begin{array} { c } 3 x - 2 y = 56 \\y = - 2 x\end{array}$

A) (0, 0)
B) (8, -16)
C) (3, -11)
D) (7, -17)
E) (5, -10)

Question 57

Solve, using the substitution method, and check. $\begin{array} { c } 4 x + y = 45 \\- 2 x + 5 y = 27\end{array}$

A) (-9, 9)
B) (4, 14)
C) (12, 6)
D) (10, 8)
E) (9, 9)

Question 58

Solve, using the substitution method, and check. $\begin{array} { c } 3 x + 4 y = 63 \\x = y\end{array}$

A) (-63, -63)
B) (10, 10)
C) (14, 9)
D) (6, 6)
E) (9, 9)

Question 59

Solve, using the substitution method, and check. $\begin{array} { c } 4 x + 3 y = - 8 \\x + y = 0\end{array}$

A) (-7, 7)
B) (13, -13)
C) (11, -11)
D) ( 8, -8)
E) (-8, 8)

Question 60

Solve, using the substitution method, and check. $\begin{array} { l } 3 x + y = 31 \\4 x - y = 25\end{array}$

A) (3, 12)
B) (16, 7)
C) (9, 8)
D) (8, 7)
E) (11, 10)

Question 61

Draw the graphs of the pair of linear equations. $\begin{array} { l } 3 x + 2 y = 20 \\2 x - 3 y = 22\end{array}$

A)
B)
C)
D)

Question 62

Draw the graphs of the pair of linear equations. $\begin{array} { l } 3 x + y = - 14 \\2 x + 5 y = 8\end{array}$

A)
B)
C)
D)

Question 63

Draw the graphs of the pair of linear equations. $\begin{array} { c } 7 x - 6 y = 13 \\4 x + 3 y = 2\end{array}$

A)
B)
C)
D)

Question 64

Draw the graphs of the pair of linear equations. Find the point of intersection. If the lines do not intersect, tell whether the lines are parallel or coincide. $\begin{array} { c } 3 x + 2 y = 38 \\x = 8\end{array}$

A)
B)
C)
D)

Question 65

Draw the graphs of the pair of linear equations. $\begin{array} { l } y = - 7 \\y = x - 2\end{array}$

A)
B)
C)
D)

Question 66

Draw the graphs of the pair of linear equations. Find the point of intersection. If the lines do not intersect, tell whether the lines are parallel or coincide. $\begin{array} { c } x - 3 y = 6 \\2 x - 6 y = 18\end{array}$

A)
B)
C)
D)

Question 67

Draw the graphs of the pair of linear equations. Find the point of intersection. If the lines do not intersect, tell whether the lines are parallel or coincide. $\begin{array} { l } 2 x - 10 y = 25 \\3 x - 15 y = 30\end{array}$

A)
B)
C)
D)

Question 68

Draw the graphs of the pair of linear equations. Find the point of intersection. If the lines do not intersect, tell whether the lines are parallel or coincide. $\begin{array} { l } 5 x - y = 36 \\x - 3 y = - 4\end{array}$

A)
B)
C)
D)

Question 69

Solve, using the substitution method, and check. $\begin{array} { c } 8 x - y = 10 \\y = - x\end{array}$ Enter your answer as an ordered pair in the form (x, y). Express your answer as fractions.

Question 70

Solve, using the substitution method, and check. $\begin{array} { c } 2 x + y = 11 \\y = 3 x\end{array}$ Enter your answer as an ordered pair in the form (x, y). Express your answer as fractions.

Question 71

Solve, using the substitution method, and check. $\begin{array} { c } 3 x + 4 y = - 16 \\x = 2 y\end{array}$ Enter your answer as an ordered pair in the form (x, y). Express your answer to one decimal place, if necessary.

Question 72

Draw the graphs of the pair of linear equations. $\begin{array} { l } y = 8 x \\y = - x + 8\end{array}$

A)
B)
C)
D)

Question 73

Draw the graphs of the pair of linear equations. Find the point of intersection. If the lines do not intersect, tell whether the lines are parallel or coincide. $\begin{array} { l } 6 x + 2 y = 36 \\3 x - 4 y = 18\end{array}$

A)
B)
C)
D)

Question 74

Draw the graphs of the pair of linear equations. Find the point of intersection. If the lines do not intersect, tell whether the lines are parallel or coincide. $\begin{array} { c } x + y = 15 \\2 x + y = 23\end{array}$

A)
B)
C)
D)

Question 75

Draw the graphs of the pair of linear equations. $\begin{array} { l } 4 x + 3 y = 6 \\5 x - y = 36\end{array}$

A)
B)
C)
D)

Question 76

Solve, using the substitution method, and check. $\begin{array} { c } 3 x - 2 y = 44 \\y = - 4 x\end{array}$ Enter your answer as an ordered pair in the form (x, y).

Question 77

Draw the graphs of the pair of linear equations. Find the point of intersection. If the lines do not intersect, tell whether the lines are parallel or coincide. $\begin{array} { c } x - y = 1 \\x + 3 y = 17\end{array}$

A)
B)
C)
D)

Question 78

Solve, using the substitution method, and check. $\begin{array} { c } 4 x + 5 y = 57 \\4 x = - 24 y\end{array}$ Enter your answer as an ordered pair in the form (x, y).

Question 79

Draw the graphs of the pair of linear equations. $\begin{array} { c } 2 x - y = 23 \\- 2 x + 3 y = - 41\end{array}$

A)
B)
C)
D)

Question 80

Draw the graphs of the pair of linear equations. Find the point of intersection. If the lines do not intersect, tell whether the lines are parallel or coincide. $\begin{aligned}y & = - x \\y - x & = 18\end{aligned}$

A)
B)
C)
D)