How do you solve by substitution x−y=−4 and x+3y=4?

2 Answers
Don't Memorise
Jun 11, 2015

The solution for the system of equations is
x=−2,y=2

Explanation:

x−y=−4
x=−4+y .....equation (1)
x+3y=4........equation (2)

Substituting equation 1 in 2 to find x
x+3y=4
−4+y+3y=4
−4+4y=4
4y=8
y=2

Substituting y in equation 1 to obtain x:
x=−4+y
x=−4+2
x=−2

Alan P.
Jun 11, 2015

(x,y)=(−2,2)

Explanation:

Given:
[1]XXXXx−y=−4
[2]XXXXx+3y=4

We can rewrite [1] as
[3]XXXXx=y−4
then substituting the expression y−4 from [3] in place of x in [2]
[4]XXXX(y−4)+3y=4
which simplifies as
[5]XXXX4y=8
or
[6]XXXXy=2
substituting 2 for y in [1], we get
[7]XXXXx−2=−4
[8]XXXXx=−2

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