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Sample edHelper.com - LinearEquations Worksheet

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Linear Equations
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 = 2 y + -4 x

4.
 y = 2 x + 5

4y = -1 + x

Solve each system of equations using the substitution method.
 5 x + 3y = -863x + y = 38
 6 16x + 9y = 195x + 8y = -25

Solve each system of equations using the substitution method.
7.
x =
 7 4
y  -
 63 2

18x - y = -628

 8 2x + 3y = -20x + 3y = -55

Solve each system of equations using the elimination method.
 9 16x - 11y = -3118x + 5y = 469
 10 17x + 14y = -107915x + 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 = -14515x + 7y = 107
 14 8x - 5y = -222x - 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 37x - 8y -273x + 5y 35
 18 5x - y -53y -305x + 2y -20
 19 7x - 2y 422x - 3y -55x + y 30

Solve each system by graphing. Find the vertices of the graph.
 20 9x - 4y -203x - y -154x - 3y -154x + y -20
 21 x + y -7x + 2y 116x - 11y 4313x - y 35
 22 2x - 3y -213x - 2y -411x - 2y 154x + y 2

Solve each system by graphing. Find the vertices of the graph.
 23 4x - 5y -122x - y -613x - 8y 2717x - 4y 3
 24 8x - 3y 463x - 2y 1911x - 5y 58
 25 4x - y 279x - 8y 555x - 2y 115y -15

Find the minimum and maximum values of the objective quantity.
 26 x + y 511x - 5y 79x - 7y -35f(x,y) = -8x + 11y - 16
 27 10x - 3y 253x - 4y -84x + 5y -21f(x,y) = -4x - 3y
 28 5x - 13y 333x + 5y 7x - y 13f(x,y) = 12x - 8y

Find the minimum and maximum values of the objective quantity.
 29 13x - 5y 87x - y 63x - 2y 159x - 4y 64f(x,y) = -9x - 9y
 30 3x + 2y -40x + y -63x - 7y 324x - 5y -15f(x,y) = -7x - 12y + 8
 31 4x - 7y 645x - y 182x - 5y 385x - 4y 27f(x,y) = -11x - 10y

Find the minimum and maximum values of the objective quantity.
 32 3x - 2y 144y -4x - y 12x - 3y 6f(x,y) = -11x - 8y
 33 4x - 5y 135y -454x -12f(x,y) = -3x - 10y
 34 x + 7y -3x + y -32x - y 9f(x,y) = 6x - 3y

Solve each system of equations.
 35 2x + 2y + 2z = -16-2x = 10-x + 5y + 2z = -10
 36 -2x + y - 2z = -64x = -24-x - 4y - z = 15
 37 -8x = 642x + 5y - z = 3x - 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 = 43x - 6y + 6z = -90

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