Question

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

Answer 1

The solution for the system of equations is
`color(red)(x = -2 , y=2`

Explanation:

`x-y=-4`
`x =color(red)( -4+y` .....equation `(1)`
`x+3y=4`........equation `(2)`

Substituting equation `1` in `2` to find `x`
`x+3y=4`
`color(red)(-4+y) +3y=4`
`-4 +4y = 4`
`4y = 8`
`color(red)(y=2`

Substituting `y` in equation `1` to obtain `x`:
`x =-4+y`
`x = -4+2`
`color(red)( x=-2`

Answer 2

`(x,y) = (-2,2)`

Explanation:

Given:
[1]`color(white)("XXXX")` `x-y = -4`
[2]`color(white)("XXXX")` `x+3y = 4`

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