Question

How do you solve this system of equations: `y+ 3= x and 3x + 4y = 16`?

Answer 1

`x=4,y=1`

Explanation:

Writing `y+3` for `x` in the second equation

`3(y+3)+4y=16`
expanding
`3y+9+4y=16`
so `7y=7`
`y=1`

so
`x=4`

Answer 2

`y=1`
`x=4`

Explanation:

The easiest way here is by substitution. We know what `x` is, because of the first equation so simply take what `x` is and substitute it for `x` in the second equation like so:

`3(y+3) +4y = 16`

Distribute the 3

`3y + 9 +4y = 16`

Combine like terms

`7y+ 9= 16`

solve for `y` by subtracting 9 from both sides then dividing both sides by 7:

`y=1`

plug 1 in for `y` into either of your original equations and solve for `x`

`x=4`