Question

How to solve for y in `5x-y=33` and `7x+y=51`?

Answer 1

`y=5x-33` and `y=-7x+51`.

First Equation:

`5x-y=33`

Subtract `5x` from both sides.

`-y=33-5x`

Multiply both sides by `-1`.

`y=-33+5x`

Rearrange.

`y=5x-33`

Second Equation:

`7x+y=51`

Substitute the `y` from the first equation

`7x+(5x-33)=51->12x-33=51`

Add `33` to both sides, and then divide by `12`

`12x=84->x=7`

Now put this into the equation for `y`

`y=5x-33->y=5*7-33=35-33->y=2`

Answer : `x=7,y=2`