Question

How do you solve the system 3x - 2y = 8 and 2x + 5y = -1?

Answer 1

`x=2, y=-1`

Explanation:

This is a clear simultaneous equation.

`3x-2y=8`
`2x+5y=-1`

In order to solve this, either the x's or the y's must be balanced. It does not matter which one you start with.

For this, I'll balance the y's:

`15x-10y=40` Every value is multiplied by 5.
`4x+10y=-2` Every value is multiplied by 2.

Both y values can now be eliminated.

`15x-10y+4x+10y=19x`
`40-2=38`

`19x=38`

Now solve for x.

`x=38/19=2`

Put the value for x back into either equation to find y.

`3x-2y=8`
`3(2)-2y=8`
`6-2y=8`
`-2y=8-6=2`

Rearrange to find y.

`-2y=2`

Divide both sides by -2.

`y=2/-2`

`y=-1`