Answer
The solution to this system of equations is $(-1, -2)$.
Work Step by Step
We need to use the substitution method to solve this system of equations. Therefore, we need to express one variable in terms of another. Let's choose to solve the first equation for $x$ in terms of $y$:
$x - 2y = 3$
We add $2y$ to both sides of the equation to isolate the $x$ variable on the left side of the equation:
$x = 2y + 3$
We can now substitute $x=2y+3$ into the second equation:
$3(2y + 3) + y = -5$
$6y + 9 + y = -5$
$(6y + y) + 9 = -5$
$7y + 9 = -5$
Subtract $9$ from both sides to isolate the $y$ term:
$7y = -14$
Solve for $y$ by dividing both sides by $7$:
$y = -2$
Now that we have the value for $y$, we can substitute this value into the first equation to solve for $x$:
$x - 2(-2) = 3$
$x + 4 = 3$
Subtract $4$ from both sides to solve for $x$:
$x = -1$
The solution to this system of equations is $(-1, -2)$.