Answer
The two graphs intersect at the point $(5, 32)$.
Work Step by Step
To find the point where two lines intersect, we will use the system of equations to solve.
Let us rewrite the equations so that the variables are on one side of the equation while the constants are on the other:
$-7x + y = -3$
$-6x + y = 2$
We want to make it so that the terms involving one of the variables is exactly the same except that they will differ in sign; then, we can eliminate one of the variables. With this in mind, we see that the two equations have the exact same $y$ term, but we need them to have opposite signs. We can accomplish this by multiplying one of the equations by $-1$. Let's use this strategy with the first equation to get:
1st equation: $ 7x - y = 3$
2nd equation: $-6x + y = 2$
Now we can add the two equations together to get:
\begin{align*}
(7x-y)+(-6x+y)&=3+2\\
x&= 5\end{align*}
Now that we have the value for $x$, we can plug this into the original equation $y = 7x - 3$ to solve for $y$:
$y = 7(5) - 3$
$y = 35 - 3$
$y = 32$
Thus, the two graphs intersect at the point $(5, 32)$.
