Answer
The solution is $(5, 2)$.
Work Step by Step
Let's solve one of the equations for one of the variables, and then use that equation to substitute into the other equation. Let's solve the second equation for $x$:
$x + 2y = 9$
Subtract $2y$ from each side of the equation to solve for $x$:
$x = -2y + 9$
We can use this equation to substitute for $x$ in the first equation. Then we can solve for $y$ first:
$2(-2y + 9) - y = 8$
Use distribution to get rid of the parentheses:
$-4y + 18 - y = 8$
Combine the $y$ terms:
$-5y + 18 = 8$
Move constants to the right side of the equation by subtracting $18$ from each side of the equation:
$-5y = -10$
Divide each side of the equation by $-5$ to solve for $y$:
$y = 2$
Now that we have the value for $y$, let's plug this value for $y$ into the first equation:
$2x - 2 = 8$
Add $2$ to each side of the equation to move constants to the right side of the equation:
$2x = 10$
Divide each side by $2$ to solve for $x$:
$x = 5$
The solution is $(5, 2)$.