Question

How do you solve 1/2(x-y) = 2 and 1/2(x+y)+1 = 0?

Answer 1

`x=1` and `y=-3`

Explanation:

Solve like simultaneous equations.

Equation 1: `1/2(x-y) = 2`
Expand the brackets to get `1/2x-1/2y=2`

Equation 2: `1/2(x+y)+1 = 0`
Expand the brackets to get `1/2x+1/2y+1=0`

`1/2x-1/2y=2`

`1/2x+1/2y+1=0`

Add the two equations together to get
`1/2x+1/2x+1/2y-1/2y+1=2`

`x+1=2`
`x=1`

Substitute this value of `x` into either Equation 1 or 2 and solve for `y`

Equation 2: `1/2(1)+1/2y+1=0`
`1/2+1/2y+1=0`
`1/2y+1=-1/2`
`1/2y=-1` `1/2`
`y = -3`