Question

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

Answer 1

`x=1` and `y=-1`

Explanation:

`1/2 x+3/4 y=-1/4`
Multiply all by 4
`2x+3y=-1`

`3/4 x+ -1/4 y=1`
`3/4x-1/4y=1`
Multiply all by 4
`3x-y=4`
`y=3x-4`

Substitute `y` into the equation
`2x+3(3x-4)=-1`
`2x+9x-12=-1`
`11x=11`
`x=1`

Substitute `x` into the equation
`y=3(1)-4`
`y=3-4`
`y=-1`