To solve the given system of equations, we can substitute the expression for \( y \) from the second equation into the first equation.
The equations are:
\[ -4x + 3y = -2 \quad (1) \] \[ y = x - 1 \quad (2) \]
Substituting equation (2) into equation (1):
\[ -4x + 3(x - 1) = -2 \]
Now, simplify the left side:
\[ -4x + 3x - 3 = -2 \]
Combining like terms gives:
\[ -x - 3 = -2 \]
Now, add 3 to both sides:
\[ -x = 1 \]
Multiplying both sides by -1 yields:
\[ x = -1 \]
Now we can find \( y \) using equation (2):
\[ y = x - 1 \] \[ y = -1 - 1 = -2 \]
Thus, the solution to the system of equations is:
\[ x = -1 \] \[ y = -2 \]