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What are x and y if $10x - 2y = -8$ and $3y - 5x = 8$ ?

1 Answer

Oct 21, 2015

$(x,y) = (-2/5,2)$

Explanation:

Given
[1] $color(white)("XXX")10x-2y = -8$
[2] $color(white)("XXX")3y-5x=8$

Rearrange [2] into standard form order:
[3] $color(white)("XXX")-5x+3y=8$

Multiply [3] by $2$ to make coefficients of $x$ in [1] and [4] additive inverses
[4] $color(white)("XXX")-10x+6y = 16$

Add [1] and [4]
[5] $color(white)("XXX")4y=8$

Divide [5] by $2$
[6] $color(white)("XXX")y=2$

Substitute $2$ fro $y$ in [1]
[7] $color(white)("XXX")10x-2(2)=-8$

[8] $color(white)("XXX")10x -4 = -8$

[9] $color(white)("XXX")10x = -4$

[10] $color(white)("XXX")x=-2/5$

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