To solve the system of equations:
- \( 2x - 2y = 6 \)
- \( 3x + 2y = 9 \)
Let's solve it step by step.
Step 1: Simplify the first equation.
Divide the first equation by 2:
\[ x - y = 3 \quad \text{(Equation 1)} \]
Step 2: Rearrange Equation 1 to express \(y\) in terms of \(x\):
\[ y = x - 3 \quad \text{(Equation 2)} \]
Step 3: Substitute Equation 2 into the second equation:
Substituting for \(y\) in Equation 2:
\[ 3x + 2(x - 3) = 9 \]
Simplifying this gives:
\[ 3x + 2x - 6 = 9 \]
Combine like terms:
\[ 5x - 6 = 9 \]
Add 6 to both sides:
\[ 5x = 15 \]
Divide by 5:
\[ x = 3 \quad \text{(Value of x)} \]
Step 4: Now substitute \(x = 3\) back into Equation 2 to find \(y\):
\[ y = 3 - 3 = 0 \quad \text{(Value of y)} \]
Final Solution: The solution to the system of equations is \(x = 3\) and \(y = 0\).
Thus, the answer is:
B: \(x = 3, y = 0\).