Question

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

Answer 1

Using substitution, we can find that `x=1` and `y=-5/2`.

Explanation:

Let's solve the second equation for one variable. We'll choose `x` first:

`x=-3/2-y`

Let's now plug that into our first equation:

`3/4(-3/2-y)-1/2y=-1/2`
`-9/8-3/4y-1/2y=-1/2`
`-9/8-3/4y-2/4y=-1/2`
`-9/8-1/4y=-1/2`
`-1/4y=-1/2+9/8`
`-1/4y=-4/8+9/8`
`(-1/4y)/(-1/4)=(5/8)/(-1/4)`
`y=-5/2`

Let's now take our y-value and put that into our equations solved for `x`:

`x=-3/2-(-5/2)`
`x=-3/2+5/2=2/2=1`

Hope this helped!