Question

How do you solve the system `x = −2y − 1` and `2x + y = −20`?

Answer 1

Given
`"[1] "x=-2y-1`
`"[2] "2x+y = -20`

We can substitute for `x` in [2] the expression for `x` in [1]
`"[3] "2(-2y-1)+y = -20`
Simplifying
`"[4] "-3y -2 = -20`
which implies
`[5] "y=6`

Substituting the value for `y` back into [1]
`"[6] "x = -2(6) -1`
implying
`"[7] "x = -13`

Solution is `(x,y) = (-13,6)`