Question

How do you solve the system using the elimination method for 3(x-y)=15 and 2x+7=7?

Answer 1

`(x,y) = (0,-5)`
`color(white)("XXXX")`by the elimination method (although the "elimination" has already been done)

Explanation:

Given
[1]`color(white)("XXXX")` `3(x-y) = 15`
[2]`color(white)("XXXX")` `2x+7 = 7`

Since `y` has already been eliminated in [2]
if we simplify [2] as
[3]`color(white)("XXXX")` `2x = 0`
`rArr`
[4]`color(white)("XXXX")` `x = 0`

We can then substitute `x=0` back into [1] to get
[5]`color(white)("XXXX")` `3(0-y) = 15`
or, after simplification:
[6]`color(white)("XXXX")` `y = -5`