Question

How do you solve the system of equations `3x - 7y = 56` and `4x + 7y = - 7`?

Answer 1

x`=7, y=-5`

Explanation:

`3x-7y=56`
`4x+7y=-7`

There are two ways to solve problem, though, the first way may not apply to every system of equations.

1st:
add the upper equation to the bottom equation like this:

`3x-7y=56`
`ul(4x+7y=-7)`
this cancels the `-7y and 7y` because they add to `0`
`3x+4x =7x`

`-7y +7y =0`

`56-7=49`

`7x=49`

Divide by `7` on both sides, you will get x=7

Replace `x " in " 4x+7y = -7` with `7`

`4(7)+7y=-7`
`28+7y=-7" "`minus 28 on both sides
`7y=-35`

`7y/7=-35/7`

y=-5

2nd:
`3x-7y=56`
`3x=56+7y`

Divide by `3` on both sides, and you will get `x=(56+7y)/3`
Replace `x " in " 4x+7y=-7` with `x=(56+7y)/3`

`4((56+7y)/3)+7y=-7`
`=(224+28y)/3+7y=-7`

`7y=(7y)/1`, so make the denominator similar to `(224+28y)/3` by multiply 3 which result of `(21y)/3`
`(224+28y)/3+(21y)/3=-7`
`(224+49y)/3=-7`

multiplying by `3` on both sides

`224+49y=-21" "` minus `224` on both sides

`49y=-245" "`divide 49 on both sides
y=-5

replace `y " in " 3x-7y=56 " with" -5`
`3x-7(-5)=56`

`3x+35=56` minus `35` on both sides

`-3x=21`

divide by `3`

x=7

sorry if it's a bit too long, but always use the second method as it's universal to the system equation. good luck!