Question

How do you solve `3y - 2x = 11` and `y + 2x = 9` using substitution?

Answer 1

`y=5 and`x=2#

Explanation:

`2x + y =9`
`-2x + 3y =11`

We need to solve `2x + y = 9` for `y`

`2x + y = 9`
`y=9 -2x`

Now substitute `-2x + 9` for `y` in `-2x + 3y =11`

`-2x + 3y =11`

`-2x + 3(-2x+9)=11`

Distribute

`-2x + (3)(-2x)+(3)(9)=11`

`-2x - 6x + 27 = 11`

`-8x + 27 = 11`

`-8x = 11 - 27`

`-8x = -16`

`x=(-16)/(-8)`

`x=2`

Now substitute `2` for `x` in `y=-2x+9`

`y=-2x + 9`

`y=-2(2)+9`

`y=-4 + 9`

`y=5`

Thus,

The answers are `y=5` and `x=2`