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

1 Answer
Alan P.
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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