Answer
$x = 6, y = 4$ or $(6, 4)$
Work Step by Step
First, rewrite both equations such that the variables are on one side of the equation and the constant is on the other:
Equation 1: $3x - 6y = -6$
Equation 2: $4x - 5y = 4$
Rewrite the equations such that one of the variables in the two equations is the same but differing in sign. To do this, multiply the first equation by $4$ and the second equation by $-3$:
Equation 1: $12x - 24y = -24$
Equation 2: $-12x + 15y = -12$
Add the equations together to eliminate the $x$ variable:
$$-9y = -36$$
Divide both sides of the equation by $-9$ to solve for $y$:
$$y = 4$$
Substitute this value of $y$ into one of the equations to solve for $x$. Use Equation 2:
$$4x - 5(4) = 4$$
Multiply to simplify:
$$4x - 20 = 4$$
Add $20$ to each side of the equation to isolate the $x$ term:
$$4x = 24$$
Divide both sides of the equation by $4$ to solve for $x$:
$$x = 6$$
