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

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Answer 1 · 2015-05-27T18:20:00

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 $(x,y) = (-13,6)$

How do you solve the system x = −2y − 1x = −2y − 1 and 2x + y = −202x + y = −20?