Answer
The solution for this system of equations is $(3, -4)$.
Work Step by Step
We can use substitution to solve this system of equations because one of the equations already has $y$ isolated to one side. We use the second equation to substitute for $y$ in the first equation:
$$2x + 3(3x - 13) = -6$$
Use distributive property first:
$$2x + 9x - 39 = -6$$
Combine like terms:
$$11x - 39 = -6$$
Add $39$ to each side of the equation to move all constants to the right side of the equation:
$$11x = 33$$
Divide by $11$ on each side to solve for $x$:
$$x = 3$$
Now that we have the value for $x$, we can plug it into the second equation to solve for $y$:
$$y = 3(3) - 13$$
Multiply first, according to order of operations:
$$y = 9 - 13$$
Subtract to solve for $y$:
$$y = - 4$$
The solution for this system of equations is $(3, -4)$.
