To solve the given system of equations:
[tex]\[
-7x - 6y = 4
\][/tex]
[tex]\[
x = -3y + 8
\][/tex]
we can follow these steps:
1. Substitute the expression for [tex]\( x \)[/tex] from the second equation into the first equation. This gives us:
[tex]\[
-7(-3y + 8) - 6y = 4
\][/tex]
2. Distribute and combine like terms:
[tex]\[
21y - 56 - 6y = 4
\][/tex]
3. Combine like terms:
[tex]\[
15y - 56 = 4
\][/tex]
4. Add 56 to both sides to isolate the term with [tex]\( y \)[/tex]:
[tex]\[
15y = 60
\][/tex]
5. Divide both sides by 15 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = 4
\][/tex]
6. Substitute the value of [tex]\( y \)[/tex] back into the second equation to solve for [tex]\( x \)[/tex]:
[tex]\[
x = -3(4) + 8
\][/tex]
7. Simplify:
[tex]\[
x = -12 + 8
\][/tex]
[tex]\[
x = -4
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
x = -4
\][/tex]
[tex]\[
y = 4
\][/tex]
