To solve the system of equations:
- \( 2x - 3y = 20 \) (Equation 1)
- \( 2x - 2y = 10 \) (Equation 2)
We can use the elimination method or the substitution method. Here, I'll use the elimination method.
First, let's eliminate \( x \) by making the coefficients of \( x \) in both equations equal. Notice that both equations have \( 2x \), so we can simply subtract one equation from the other.
Subtract Equation 2 from Equation 1: \[ (2x - 3y) - (2x - 2y) = 20 - 10 \] \[ -3y + 2y = 10 \] \[ -y = 10 \] \[ y = -10 \]
Now that we have \( y = -10 \), we can substitute this value back into one of the original equations to find \( x \). We can use Equation 2: \[ 2x - 2(-10) = 10 \] \[ 2x + 20 = 10 \] \[ 2x = 10 - 20 \] \[ 2x = -10 \] \[ x = -5 \]
Finally, the solution to the system of equations is: \[ x = -5, \quad y = -10 \]
Thus, the solution is \( (x, y) = (-5, -10) \).