Answer
$x = \frac{1}{3}, y = 4$ or $(\frac{1}{3}, 4)$
Work Step by Step
$\begin{cases} 3x + y = 5 \\ 3x - 2y = -7 \end{cases}$
We solve for $y$ from the first equation by subtracting $3x$ from both sides: $3x + y - 3x = 5 - 3x$
$y = 5 - 3x$
Now that we've solved for y we substitute $5-3x$ for y in the second equation:
$3x - 2(5-3x)=-7$
$3x - 10 + 6x = -7$
$9x = 3$
$x = \frac{1}{3}$
Now that we've found x we substitute $\frac{1}{3}$ for x in $y = 5-3x$:
$y = 5 - 3\times\frac{1}{3}$
$y = 5 - 1 = 4$
So the solution is $x = \frac{1}{3}, y = 4$ or $(\frac{1}{3}, 4)$
