Question

How do you solve the system `2x+4y=6` and `2x+y= -3` by substitution?

Answer 1

x=-3, y=3

Explanation:

`2x+4y=6` eq 1
`2x+y=-3` eq 2
From eq 2, make y the subject:
`y=-3+2x`
Substitute y from above in eq 1
`2x+4(-3+2x)=6`
`2x-12+8x=6`
`2x-8x=6+12`
`-6x=18`
`x=-18/6`
`x=-3`
Now, substitute x=-3 in eq 1 or eq 2. Lets use eq 1.
`2(-3)+4y=6`
Now solve for y
`-6+4y=6`
`4y=6+6`
`4y=12`
`y=12/4`
`y=3`
Check for answer:
use eq 1 or eq 2
`2(-3) + 3 = -6+3=-3`
So the answers x=-3 and y=3 are correct