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Solving Simultaneous Equations by Substitution Method

Solve each system of equations by substitution method. Show work by step by step solutions.

1) x + 3y = 2
3x + 9y = 6

2) 4x - 2y = 2
2x - y = 1

3) x/4 - y/4 = -1
x + 4y = -9

4) x/6 - y/2 = 1/3
x + 2y = -3

5) 2x = 3y + 4
4x = 3 - 5y

6) 4x = 3y + 8
2x = -14 + 5y

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Solution Preview

Solutions:

1) x + 3y = 2 - [A]
3x + 9y = 6 - [B]

Multiplying [A] with 3, we get 3x +9y = 6 which is the same equation as that of [B]. Therefore, this pair of simultaneous equations have no solution.

2) 4x - 2y = 2 [A]
2x - y = 1 [B]

Multiplying [B] with 2, we get 4x -2y = 2 which is the same equation as that of [A]. Therefore, this pair of simultaneous equations have no solution.

3) x - y = -1 [A]
4 4

x + 4y = -9 [B]

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Solution Summary

This solution is comprised of a detailed step-by-step calculation of the given word problems and provides students with a clear perspective of solving linear simultaneous equations in Algebra.

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