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

1 Answer

Oct 21, 2015

$(x, y) = (- \frac{2}{5}, 2)$ $(x,y) = (-2/5,2)$

Explanation:

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

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

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

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

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

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

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

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

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

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