Answer :

GinnyAnswer
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]

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