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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

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    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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