How do you solve 5x + 8y = 7 and x + y = 2 using substitution?

2 Answers
Apr 24, 2016

x=3, y= -1

Explanation:

given x+y=2
y= 2 - x (eq. 1)

given 5x+8y=7 (eq.2)

substitute eq. 1 in eq. 2

5x + 8(2-x) =7
5x + 16 - 8x = 7 (open the bracket)
-3x=7-16= -9
x= -9/ -3 = 3

eq 1-
y= 2-3= -1

so x=3, y= -1

Apr 24, 2016

(x,y)=(3,-1)
See below for method of solution by substitution.

Explanation:

If x+y=2
then y=2-x
and
color(white)("XXX")(2-x) can be substituted for y in 5x+8y=7

This would give:
color(white)("XXX")5x+8(2-x)=7

color(white)("XXX")5x+16-8x=7

color(white)("XXX")-3x=-9

color(white)("XXX")x= 3

Then, returning to y=2-x
we have
color(white)("XXX")y=2-3 =-1