Answer
The solution to this system of equations is $(-9, -26)$.
Work Step by Step
In the first equation, we already have an expression for $y$ that we can substitute into the second equation to find $x$. Let us substitute $y=3x+1$ into the second equation:
$2x-y=8\\
2x - (3x + 1) = 8$
Use distributive property to get rid of the parentheses:
$2x - 3x - 1 = 8\\
-x-1=8$
Add $1$ to both sides to isolate constants to the right side of the equation:
$-x-1+1 =8+1\\
-x=9$
Divide both sides by $-1$ to solve for $x$:
$x = -9$
Now that we have a value for $x$, we can substitute it into the first equation to solve for $y$:
$y=3x+1\\
y = 3(-9) +1\\
y=-27+1\\
y=-26$
The solution to this system of equations is $(-9, -26)$.
