Answer
The solution is $(10, -1)$.
Work Step by Step
We are asked to use the substitution method to solve this system of equations. The first thing we want to do is to isolate one of the variables in one of the equations. Let's try to isolate the $x$ in the first equation. First, we subtract $6y$ from both sides of the equation:
$2x = -6y + 14$
Divide both sides by $2$:
$x = -3y + 7$
Substitute this expression where we see $x$ in the second equation:
$4(-3y + 7) - 8y = 48$
Use the distributive property:
$-12y + 28 - 8y = 48$
Combine like terms on the left side of the equation:
$-20y + 28 = 48$
Subtract $28$ from each side of the equation:
$-20y = 20$
Divide each side of the equation by $-20$:
$y = -1$
Now that we have the value of $y$, we plug in this number into one of the equations to find the value of $x$. Let's use the first equation:
$2x + 6(-1) = 14$
Multiply to simplify:
$2x - 6 = 14$
Add $6$ to each side of the equation:
$2x = 20$
Divide each side of the equation by $2$:
$x = 10$
The solution is $(10, -1)$.