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How do you solve the following equations by substitution: $8 x - 4 y = 16$ $8x - 4y = 16$ and $y = 2 x - 4 ?$ $y = 2x - 4?$ ?

1 Answer

Oct 21, 2015

There are infinitely many solutions to this pair of equations. (See below for demonstration using substitution).

Explanation:

Given:
[1] $XXX 8 x - 4 y = 16$ $color(white)("XXX")8x-4y=16$
[2] $XXX y = 2 x - 4$ $color(white)("XXX")y=2x-4$

Substituting $(2 x - 4)$ $(2x-4)$ from [2] for $y$ $y$ in [1]
[3] $XXX 8 x - 4 (2 x - 4) = 16$ $color(white)("XXX")8x-4(2x-4)=16$

Simjplifying
[4] $XXX 16 = 16$ $color(white)("XXX")16 = 16$

Since this is true for all pairs $(x, y)$ $(x,y)$ there is no unique solution.
(The equations represent the same line).

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