To solve the system of equations, we can substitute the expression for \( y \) from the first equation into the second equation. The two equations are:
- \( y = 2x - 3 \)
- \( 4x - 3y = 31 \)
Substituting the first equation into the second:
\[ 4x - 3(2x - 3) = 31 \]
Now, simplify the equation:
\[ 4x - 6x + 9 = 31 \]
Combine like terms:
\[ -2x + 9 = 31 \]
Subtract 9 from both sides:
\[ -2x = 22 \]
Now, divide by -2:
\[ x = -11 \]
Now, substitute \( x = -11 \) back into the first equation to find \( y \):
\[ y = 2(-11) - 3 \] \[ y = -22 - 3 \] \[ y = -25 \]
Therefore, the solution to the system of equations is:
\[ (x, y) = (-11, -25) \]
So, the final answer is:
The solution to the system is (−11)(−25).