How do you solve #8x = -2y - 10# and #2x = 4y# using substitution?

1 Answer
Alan P.
May 10, 2016

#(x,y)=color(blue)(""(-10/9,-5/9))#

Explanation:

Given:
[1]#color(white)("XXX")8x=-2y-10#
[2]#color(white)("XXX")2x=4y#

Dividing both sides of [2] by 2
[3]#color(white)("XXX")x=2y#

From [3] we see that we can substitute #2y# anywhere for #x#
and specifically we can substitute #2y# for #x# in [1] to get
[4]#color(white)("XXX")8(2y)=-2y-10#

Simplifying:
[5]#color(white)("XXX")16y=-2y-10#

[6]#color(white)("XXX")18y=-10#

[7]#color(white)("XXX")y=-5/9#

We can now substitute #(-5/9)# for #y# in [3] to get
[8]#color(white)("XXX")x=2(-5/9)=-10/9#

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