Question

How do you solve the system `2x+y=-9` and `3x+y=11`?

Answer 1

Noticing the same term in `y` in both equations, we can eliminate `y` quickly as follows:

Subtract the first equation from the second to get:

`x = (3x+y)-(2x+y) = 11 - (-9) = 20`

Substitute this value of `x` into the first equation to get:

`-9 = (2xx20)+y = 40+y`

Subtract `40` from both sides to get:

`y = -9 -40 = -49`

As a quick check, substitute these values for `x` and `y` into the left hand side of the second equation:

`3x+y = (3xx20)+(-49) =60-49 = 11`