To solve the given system of equations:
1. Understand the equations:
[tex]\[
\begin{array}{l}
8x - 3y = -22 \\
y = 10 + 4x
\end{array}
\][/tex]
2. Substitute [tex]\( y \)[/tex] from the second equation into the first equation:
Since [tex]\( y = 10 + 4x \)[/tex], substitute [tex]\( 10 + 4x \)[/tex] for [tex]\( y \)[/tex] in the first equation:
[tex]\[
8x - 3(10 + 4x) = -22
\][/tex]
3. Simplify the equation:
Expand and simplify the equation:
[tex]\[
8x - 3 \cdot 10 - 3 \cdot 4x = -22
\][/tex]
[tex]\[
8x - 30 - 12x = -22
\][/tex]
[tex]\[
8x - 12x = -22 + 30
\][/tex]
[tex]\[
-4x = 8
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Divide both sides by -4:
[tex]\[
x = -2
\][/tex]
5. Find [tex]\( y \)[/tex]:
Substitute [tex]\( x = -2 \)[/tex] back into the second equation [tex]\( y = 10 + 4x \)[/tex]:
[tex]\[
y = 10 + 4(-2)
\][/tex]
[tex]\[
y = 10 - 8
\][/tex]
[tex]\[
y = 2
\][/tex]
6. Conclusion:
The solution to the system of equations is [tex]\( x = -2 \)[/tex] and [tex]\( y = 2 \)[/tex].
Thus, the final answer is:
[tex]\(\boxed{(-2, 2)}\)[/tex]
