To solve the system of equations
- \( y = 2x - 3 \)
- \( 4x - 3y = 31 \)
we can substitute the expression for \( y \) from the first equation into the second equation.
Substituting \( y = 2x - 3 \) into \( 4x - 3y = 31 \):
\[ 4x - 3(2x - 3) = 31 \]
Now, distribute the \(-3\):
\[ 4x - 6x + 9 = 31 \]
Combine like terms:
\[ -2x + 9 = 31 \]
Now, isolate \( x \):
\[ -2x = 31 - 9 \] \[ -2x = 22 \] \[ x = -11 \]
Now that we have \( x = -11 \), we can substitute it back into the equation for \( y \):
\[ y = 2(-11) - 3 \] \[ y = -22 - 3 \] \[ y = -25 \]
So the solution to the system of equations is \( x = -11 \) and \( y = -25 \).
The solution to the system is \((-11, -25)\).