To solve the system of equations given by:
- \( 8x - 3y = -22 \) (Equation 1)
- \( y = 10 + 4x \) (Equation 2)
we can substitute Equation 2 into Equation 1.
Substituting \( y \) from Equation 2 into Equation 1:
\[ 8x - 3(10 + 4x) = -22 \]
Now, distribute the \(-3\):
\[ 8x - 30 - 12x = -22 \]
Combine like terms:
\[ 8x - 12x - 30 = -22 \]
This simplifies to:
\[ -4x - 30 = -22 \]
Next, add 30 to both sides:
\[ -4x = 8 \]
Now, divide by \(-4\):
\[ x = -2 \]
Now that we have \(x\), we can find \(y\) using Equation 2:
\[ y = 10 + 4(-2) \] \[ y = 10 - 8 \] \[ y = 2 \]
Thus, the solution to the system of equations is:
\[ \boxed{(-2, 2)} \]