How do you solve by substitution #0.3x-0.2y=0.5# and #x-2y= -5#?

1 Answer
Alan P.
Jun 15, 2015

By simplifying and re-arranging the terms, we get
#(x,y) = (5,5)#

Explanation:

[1]#color(white)("XXXX")##0.3x-0.2y=0.5#
[2]#color(white)("XXXX")##x-2y = -5#

I would suggest the first thing to do is to simplify [1] by multiplying everything by 10
[3]#color(white)("XXXX")##3x-2y =5#

In order to use substitution, re-arrange [2] to isolate #x#
[3]#color(white)("XXXX")##x = 2y-5#

Substitute #2y-5# for #x# in [3]
[4]#color(white)("XXXX")##3(2y-5) -2y = 5#
Simplify
[5]#color(white)("XXXX")##4y -15 = 5#
[6]#color(white)("XXXX")##y = 5#

Using [6], substitute #5# for #y# in [2]
[7]#color(white)("XXXX")##x-2(5) = -5#
[8]#color(white)("XXXX")##x=5#

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