Question

How do you solve the system of equations `5x+3y=-10` and `3x+5y=-6`?

Answer 1

`y=0` and `x=-2`

Explanation:

`5x+3y=-10`
`3x+5y=-6`

Let us eliminate `x` first so we can solve for `y`. To do this, multiply the top equation by `3` and bottom equation by `5`:

`15x+9y=-30`
`15x+25y=-30`

Subtract equations away from each other:

`0+(-16y)=0`
`-16y=0`
`y=0/-16`
`y=0`

Substitute value of `y` back into one of the original equations:

`5x+3y=-10`
`5x+3(0)=-10`
`5x=-10`
`x=-10/5`
`x=-2`

Double check solutions by plugging in the values of `x=-2` and `y=0` into the original equations to see whether you get `-10` and `-6`.