Question

How do you solve the system of equations `2x + 5y = - 1` and `3x + 2y = 4`?

Answer 1

`x=2`
`y=-1`

See below

Explanation:

`2x+5y=−1`multiply by 3
`3x+2y=4` multiply by 2 and subtract

`3*(2x+5y)=3*(−1)` equals `6x+15y=-3`
`2*(3x+2y)=2*4` . . . . . equals `6x+4y=8`
subtract: `11y=-11`
`y=-1`

now substitute back in
`3x+2(-1)=4`
`3x=6`
`x=2`

`x=2`
`y=-1`

Answer 2

`x=2`, `y=-1`

Explanation:

`color(white)(+)2x+5y=-1`
`color(white)(+)`
`color(white)(+)3x+2y=4`
................................................

Let's multiply the top equation by `1.5`

`color(white)(+)3x+7.5y=-1.5`
`color(black)(-)`
`color(white)(+)3x+2y=4`
................................................

`color(white)(0)5.5y=-5.5`

divide by `5.5` on both sides

`y=-1`

now we should solve for `x`

`2x+5y=-1`

`2x+5(-1)=-1`

`2x-5=-1`

`2x=4`

`x=2`

Just to check our work, let' solve the second equation, using `2` and `-1` for `x` and `y`

`3x+2y=4`

`3(2)+2(-1)` should equal `4`

`6-2`

`4=4`

We were right! `x=2`, `y=-1`