Question

How do you solve the system 3x+2y=4 and 4x+3y=7?

Answer 1

`x=-2` and `y=5`

Explanation:

You can begin by subtracting the first equation from the second, which simplifies your operations. Doing so leaves you with `x+y=3`.

You can write `x` as `x=3-y` and substitute in whichever equation you prefer:
`4(3-y)+3y=7`
`12-4y+3y=7`
`12-y=7`
`-y=7-12=-5`
`y=5`

After finding `y` you can return to `x=3-y` and substitute `y`.

`x=3-5`
`x=-2`

So your solution is `S={(-2,5)}`