Certainly! To solve the system of equations:
[tex]\[
\begin{array}{l}
-7x - 6y = 4 \\
x = -3y + 8 \\
\end{array}
\][/tex]
we will follow these steps:
1. Substitute the expression for [tex]\( x \)[/tex] from the second equation into the first equation.
The second equation gives:
[tex]\[
x = -3y + 8
\][/tex]
Substitute [tex]\( x = -3y + 8 \)[/tex] into the first equation:
[tex]\[
-7(-3y + 8) - 6y = 4
\][/tex]
2. Simplify the resulting equation.
Distribute the [tex]\(-7\)[/tex] through the terms inside the parentheses:
[tex]\[
21y - 56 - 6y = 4
\][/tex]
Combine like terms:
[tex]\[
15y - 56 = 4
\][/tex]
3. Solve for [tex]\( y \)[/tex].
Add 56 to both sides to isolate the term with [tex]\( y \)[/tex]:
[tex]\[
15y = 60
\][/tex]
Divide both sides by 15 to find [tex]\( y \)[/tex]:
[tex]\[
y = 4
\][/tex]
4. Substitute [tex]\( y \)[/tex] back into the second equation to find [tex]\( x \)[/tex].
Use the value of [tex]\( y = 4 \)[/tex] in the second equation:
[tex]\[
x = -3(4) + 8
\][/tex]
Simplify:
[tex]\[
x = -12 + 8
\][/tex]
[tex]\[
x = -4
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
x = -4, \quad y = 4
\][/tex]
