To solve the system of equations
- \( 8x - 3y = -22 \)
- \( y = 10 + 4x \)
we can substitute the expression for \( y \) from the second equation into the first equation.
Substituting \( y \) in the first equation gives:
\[ 8x - 3(10 + 4x) = -22 \]
Now, distribute the \(-3\):
\[ 8x - 30 - 12x = -22 \]
Combine like terms:
\[ -4x - 30 = -22 \]
Next, add 30 to both sides:
\[ -4x = 8 \]
Now, divide both sides by \(-4\):
\[ x = -2 \]
Now that we have \( x \), we can substitute it back into the second equation to find \( y \):
\[ y = 10 + 4(-2) \]
Calculating this gives:
\[ y = 10 - 8 = 2 \]
So, the solution to the system of equations is:
\[ (x, y) = (-2, 2) \]