Substitution: Solve each system by substitution.

1)
\[
\begin{align}
y &= -8x - 24 \\
y &= 4x + 24
\end{align}
\]

Substitute \( y = 4x + 24 \) into the first equation:

\[
\begin{align}
-8x - 24 &= 4x + 24 \\
-8x - 4x &= 24 + 24 \\
-12x &= 48
\end{align}
\]

\[
x = -\frac{48}{12} = -4
\]

Substitute \( x = -4 \) back into \( y = 4x + 24 \):

\[
y = 4(-4) + 24 = -16 + 24 = 8
\]

Solution: \( x = -4, \, y = 8 \)

Let's solve this system of equations using substitution step-by-step:

We have two equations:
1) [tex]\( y = -8x - 24 \)[/tex]
2) [tex]\( y = 4x + 24 \)[/tex]

Since both equations are already solved for [tex]\( y \)[/tex], we can set them equal to each other:
[tex]\[ -8x - 24 = 4x + 24 \][/tex]

Next, we'll move all terms involving [tex]\( x \)[/tex] to one side of the equation to solve for [tex]\( x \)[/tex]:
[tex]\[ -8x - 4x = 24 + 24 \][/tex]

This simplifies to:
[tex]\[ -12x = 48 \][/tex]

Now, we'll solve for [tex]\( x \)[/tex] by dividing both sides by -12:
[tex]\[ x = \frac{48}{-12} \][/tex]

This gives us:
[tex]\[ x = -4 \][/tex]

With [tex]\( x \)[/tex] found, we can substitute it back into either equation to find [tex]\( y \)[/tex]. Let's use the first equation:
[tex]\[ y = -8x - 24 \][/tex]

Substituting [tex]\( x = -4 \)[/tex] into the equation, we get:
[tex]\[ y = -8(-4) - 24 \][/tex]
[tex]\[ y = 32 - 24 \][/tex]
[tex]\[ y = 8 \][/tex]

So, the solution to the system of equations is [tex]\( x = -4 \)[/tex] and [tex]\( y = 8 \)[/tex].