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# Algebra: Substitution and Elimination

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Solve each system by substitution:

1. 4x+5y=7
9y=31+2x

Solve each system by elimination:

1. 12x-5y=9
3x-8y= -18

https://brainmass.com/math/algebra/algebra-substitution-elimination-451456

#### Solution Preview

I. Solve each system by substitution:

The method of substitution requires: 1. solving one of the equations in the system for a variable; 2. the next step is to substitute this solution in the other equation in place of that variable. Solve for the remaining variable and perform a check.

Let's perform step 1:
4x + 5y = 7
4x + 5y - 5y = 7 - 5y
4x = 7 - 5y
4x/4 = (7 - 5y)/4
x = 7/4 - 5/4 y

Substitute 7/4 - 5/4 y for x in 9y = 31 + 2x:
9y = 31 + 2(7/4 - 5/4 y)
9y = 31 + 7/2 - 5/2 y
9y = 69/2 - ...

#### Solution Summary

This solution provides a step-by-step explanation of how to solve the given algebra problems.

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