Answer
$r = -6$, $s = -6$
Work Step by Step
Given $r + s = -12$ and $4r - 6s = 12$.
Solve for $r$ in the first equation by subtracting $s$ to give:
$r = -s - 12$.
Substitute $-s-12$ into the second equation:
$4(-s - 12) - 6s = 12$
Now the equation is in terms of a single variable, solve for the variable:
$4(-s - 12) - 6s = 12$ : distribute $4$
$-4s - 48 - 6s = 12$ : collect like terms
$-10s - 48 = 12$ : add $48$ to both sides
$-10s = 60$ : divide by $-10$
$s = -6$
Substitute $s = -6$ into earlier equation: $r + s = - 12$.
$r + (-6) = -12$ : solve
$r - 6 = -12$ : add 6
$r = -6$
Giving, $r = -6$, $s = -6$
