What are x and y if 10x - 2y = -810x2y=8 and 3y - 5x = 83y5x=8?

1 Answer
Oct 21, 2015

(x,y) = (-2/5,2)(x,y)=(25,2)

Explanation:

Given
[1]color(white)("XXX")10x-2y = -8XXX10x2y=8
[2]color(white)("XXX")3y-5x=8XXX3y5x=8

Rearrange [2] into standard form order:
[3]color(white)("XXX")-5x+3y=8XXX5x+3y=8

Multiply [3] by 22 to make coefficients of xx in [1] and [4] additive inverses
[4]color(white)("XXX")-10x+6y = 16XXX10x+6y=16

Add [1] and [4]
[5]color(white)("XXX")4y=8XXX4y=8

Divide [5] by 22
[6]color(white)("XXX")y=2XXXy=2

Substitute 22 fro yy in [1]
[7]color(white)("XXX")10x-2(2)=-8XXX10x2(2)=8

[8]color(white)("XXX")10x -4 = -8XXX10x4=8

[9]color(white)("XXX")10x = -4XXX10x=4

[10]color(white)("XXX")x=-2/5XXXx=25