Question

How do you solve `x + y =1` and `2x-y=-2` using substitution?

Answer 1

By eliminating `x` in the expression `x+y=1`, we get

`x = 1-y`, which we can plug in the second expression:

`2(1-y)-y=-2`

`2-2y-y=-2`

`2-3y=-2`

`-3y+2=-2`

`-3y=-4`

`y=4/3`

Knowing `y`, we can now find `x` by plugging the `y`-value into any of the above equations. For example, by plugging `y=4` into the first equation, `x+y=1`, we get

`x+4/3=1`

`x=-1/3`

Explanation:

We can check whether these values satisfy the equations by plugging them back in:

First: `x+y=1`

`-1/3 + 4/3 = 1 -> 4/3-1/3 = 1 -> (12-3)/(9) = 1 -> 9/9 = 1`

Second: `2x-y=-2`

`2(-1/3)-4/3=-2 -> -2/3-4/3 = -2 -> -18/9 = -2`