We can solve this system of equations by substituting the value of y from the second equation into the first equation.
From the second equation, we have y = 10 + 4x.
Substituting this into the first equation:
8x - 3(10 + 4x) = -22.
Now, we can distribute the -3:
8x - 30 - 12x = -22.
Combining like terms, we have:
-4x - 30 = -22.
Adding 30 to both sides:
-4x = 8.
Dividing by -4:
x = -2.
Now that we have the value of x, we can substitute it back into the second equation to find y:
y = 10 + 4(-2).
Simplifying:
y = 10 - 8.
y = 2.
Therefore, the solution to the system of equations is x = -2 and y = 2.