We are asked to solve the following system of linear equations using the substitution method: $x + 5y = -21$ $-5x + 7y = -23$

1. Problem Description

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

$x + 5y = -21$

$-5x + 7y = -23$

2. Solution Steps

First, we solve the first equation for $x$:

$x + 5y = -21$

$x = -21 - 5y$

Next, we substitute this expression for $x$ into the second equation:

$-5x + 7y = -23$

$-5(-21 - 5y) + 7y = -23$

$105 + 25y + 7y = -23$

$32y = -23 - 105$

$32y = -128$

$y = \frac{-128}{32}$

$y = -4$

Now, we substitute $y = -4$ into the equation $x = -21 - 5y$ to find $x$:

$x = -21 - 5(-4)$

$x = -21 + 20$

$x = -1$

Thus, the solution is $x = -1$ and $y = -4$.

3. Final Answer

The solution is $x = -1$ and $y = -4$.

We can write it as $(-1, -4)$.