Solve each system by the substitution method?

Question

x+3y=2
-x+y=1

Thanks for your help..

Answer 1

x+3y=2
-x+y=1
x=2-3y
-(2-3y)+y=1
-2+3y+y=1
4y=1+2
4y=3
y=3/4

x=2-3(3/4)
x=2-9/4
x=8-9/4
x=-1/4

Answer 2

Okay, if it was elimination, it would be really easy, I'll use it for justification later.

First eq: x + 3y = 2

Therefore x = 2 - 3y
-------------------------

Substitute this x value into the next equation:

-x + y = 1

Therefore -(2 - 3y) + y = 1
Therefore -2 + 3y + y = 1
Therefore 4y = 3
Therefore y = 3/4 = 0.75
---------------------------------

Substitute the y value into either equation to find the value of x.

x + 3y = 2
Therefore x + 3 (.75) = 2
Therefore x + 2.25 = 2
Therefore x = -0.25 = -1/4
-----------------------------------

Therefore x = -0.25, y = 0.75
=======================

Justification (Using elimination method)

Mix the two equations together

(x + 3y) + (-x + y) = 2 + 1
Therefore x-x + 4y = 3
Therefore 4y = 3
Therefore y = 3/4 = 0.75

Then you substitute back into the equation like before.

Hope that helps :) I like to use communication. Perhaps not all of it is necessary.

Answer 3

x = y - 1
y - 1 + 3y = 2
4y = 3
y = 3/4
x = - 1/4

Answer 4

y = 1+x ==>
x + 3(1 + x) = 2
4x + 3 = 2
4x = -1
x = -1/4
y = 3/4

Answer 5

y = 3/4
x = -1/4