Solving Systems of Equations Worksheets with Three Variables - Free Printable

Educational worksheet: Solving Systems of Equations Worksheets with Three Variables. Download and print for classroom or home learning activities.

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I'll solve each system of equations using the elimination method. Let me work through them step by step.

Problem 1:
-4x + 3y + 2z = 25
2x - 7y + 3z = 17
-8x - 5y + 3z = -5

Let me eliminate z first from equations 1 and 2:
Multiply eq1 by 3: -12x + 9y + 6z = 75
Multiply eq2 by 2: 4x - 14y + 6z = 34
Subtract: (-12x + 9y + 6z) - (4x - 14y + 6z) = 75 - 34
-16x + 23y = 41 ... (A)

Now eliminate z from equations 2 and 3:
Eq2: 2x - 7y + 3z = 17
Eq3: -8x - 5y + 3z = -5
Subtract: (2x - 7y + 3z) - (-8x - 5y + 3z) = 17 - (-5)
10x - 2y = 22
5x - y = 11
y = 5x - 11 ... (B)

Substitute (B) into (A):
-16x + 23(5x - 11) = 41
-16x + 115x - 253 = 41
99x = 294
x = 294/99 = 98/33 ≈ 2.97

Wait, let me recalculate more carefully...

Parent Tip: Review the logic above to help your child master the concept of substitution and elimination worksheet.

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