How do solve the following linear system?: 3x – 4y = 7, x-y=2 ?

1 Answer
May 16, 2018

(x,y)=(+1,-1)

Explanation:

Given
[1]color(white)("XXX")3x-4y=7
[2]color(white)("XXX")x-y=2

There are several ways to solve this but since it was asked under "Systems Using Substitution", we will approach it that way:

Rearrange [2] into an equation in terms of x
[3]color(white)("XXX")x=y+2

Now substitute (y+2) for x in [1]
[4]color(white)("XXX")3(y+2)-4y=7

Expanding and simplifying [4]
[5]color(white)("XXX")-y+6=7
or
[6]color(white)("XXX")y=-1

Now substitute (-1) for y back in [2] (or you could have used [1])
[7]color(white)("XXX")x-(-1)=2
Simplifying:
[8]color(white)("XXX")x=1