Question

How do you solve `5x + y = 8` and `–4x – 4y = – 16` using substitution?

Answer 1

`x=1` and `y=3`

Explanation:

So always when you try to solve systems, if you find either a single y or x then use the substitution, just something I always do. Anyway so here we have

`5x+y=8`
`-4x-4y=-16`

And in the first one we have a single y ( shown below)

`5x+color(red)(y)=8`
`-4x-4y=-16`

Now we re-write it to get:

`color(red)(y) =8-5x`
`-4x-4y=-16`

Put this equation :
`color(red)(y) =8-5x`

into the other to get:

`-4x-4(8-5x)=-16`

Simplify:

`-4x-32+20x=-16`

Simplify more:

`16x=16`

Divide 16 on both sides to get:

`x=1`

Now put that into any equation to get:

`5+y=8`

Simplify to get

y=3

Now check you work by putting in the numbers into the other equation to get:

`-4(1)-4(3)=-16`
`-4-12=-16`

So it's right with

`x=1`
`y=3`

Hope this helps!