We are asked to solve the following system of equations using the substitution method: $-x + 6y = -13$ (1) $7x - y = 50$ (2)

1. Problem Description

We are asked to solve the following system of equations using the substitution method:

$-x + 6y = -13$ (1)

$7x - y = 50$ (2)

2. Solution Steps

We will solve equation (2) for $y$:

$7x - y = 50$

$y = 7x - 50$

Now we substitute this expression for $y$ into equation (1):

$-x + 6(7x - 50) = -13$

$-x + 42x - 300 = -13$

$41x = 287$

$x = \frac{287}{41}$

$x = 7$

Now we substitute $x = 7$ back into the equation $y = 7x - 50$:

$y = 7(7) - 50$

$y = 49 - 50$

$y = -1$

So the solution is $x = 7$ and $y = -1$. We can check this in the original equations:

$-x + 6y = -7 + 6(-1) = -7 - 6 = -13$

$7x - y = 7(7) - (-1) = 49 + 1 = 50$

Both equations are satisfied.

3. Final Answer

(7, -1)