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Name _____________________________
Date ___________________

Linear Equations
(Answer ID # 0882164)
Graph each system of equations and state its solution.
1.  
y =  
1

2
x   -  
15

2

2x + y = 5
2.   5x - 4y = -16
y =  
5

4
x   +  4

Graph each system of equations and state its solution.
3.   x - 3y = -8
2 =  2y  +  -4x
4.  
y =  2x   +  5

4y = -1 + x

Solve each system of equations using the substitution method.
5.   x + 3y = -86
3x + y = 38
6.   16x + 9y = 195
x + 8y = -25

Solve each system of equations using the substitution method.
7.  
x =  
7

4
y  -  
63

2

18x - y = -628
8.   2x + 3y = -20
x + 3y = -55

 

Solve each system of equations using the elimination method.
9.   16x - 11y = -31
18x + 5y = 469
10.   17x + 14y = -1079
15x + 14y = -1013

Solve each system of equations using the elimination method.
11.   5y = -112 + 3x
142

3
  +  
11

3
y  = x
12.   -2x = 36 + 4y
y =  
-8

9
x   -  
62

3

Solve each system of equations using any method.
13.   7x + 9y = -145
15x + 7y = 107
14.   8x - 5y = -22
2x - y = -10

Solve each system of equations using any method.
15.  
y =  
-1

2
x   +  
93

2

2x + y = 72
16.  
y =  
4

3
x   +  
47

3

18x + 17y = -181

 

Solve each system by graphing. Find the vertices of the graph.
17.   4x - 3y    37
x - 8y    -27
3x + 5y    35
18.   5x - y    -5
3y    -30
5x + 2y    -20
19.   7x - 2y    42
2x - 3y    -5
5x + y    30

Solve each system by graphing. Find the vertices of the graph.
20.   9x - 4y    -20
3x - y    -15
4x - 3y    -15
4x + y    -20
21.   x + y    -7
x + 2y    11
6x - 11y    43
13x - y    35
22.   2x - 3y    -21
3x - 2y    -4
11x - 2y    15
4x + y    2

Solve each system by graphing. Find the vertices of the graph.
23.   4x - 5y    -12
2x - y    -6
13x - 8y    27
17x - 4y    3
24.   8x - 3y    46
3x - 2y    19
11x - 5y    58
25.   4x - y    27
9x - 8y    55
5x - 2y    11
5y    -15

 

Find the minimum and maximum values of the objective quantity.
26.   x + y    5
11x - 5y    7
9x - 7y    -35
f(x,y) = -8x + 11y - 16
27.   10x - 3y    25
3x - 4y    -8
4x + 5y    -21
f(x,y) = -4x - 3y
28.   5x - 13y    33
3x + 5y    7
x - y    13
f(x,y) = 12x - 8y

Find the minimum and maximum values of the objective quantity.
29.   13x - 5y    87
x - y    6
3x - 2y    15
9x - 4y    64
f(x,y) = -9x - 9y
30.   3x + 2y    -40
x + y    -6
3x - 7y    32
4x - 5y    -15
f(x,y) = -7x - 12y + 8
31.   4x - 7y    64
5x - y    18
2x - 5y    38
5x - 4y    27
f(x,y) = -11x - 10y

Find the minimum and maximum values of the objective quantity.
32.   3x - 2y    14
4y    -4
x - y    1
2x - 3y    6
f(x,y) = -11x - 8y
33.   4x - 5y    13
5y    -45
4x    -12
f(x,y) = -3x - 10y
34.   x + 7y    -3
x + y    -3
2x - y    9
f(x,y) = 6x - 3y

 

Solve each system of equations.
35.   2x + 2y + 2z = -16
-2x = 10
-x + 5y + 2z = -10
36.   -2x + y - 2z = -6
4x = -24
-x - 4y - z = 15
37.   -8x = 64
2x + 5y - z = 3
x - 12y - 6z = 22

Solve each system of equations.
38.   -2x - 9y + 4z = -60
-7x + 11y + 10z = 45
-12x - y - 6z = -42
39.   -8x + 12y - 4z = 68
-2x + 11y + 7z = -71
-9x - 8y + 5z = 34
40.   x - 10y + 3z = -78
-4x - 4y - z = 4
3x - 6y + 6z = -90

 

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