Apologies for any confusion earlier. Let's walk through the solution step by step in plain text:
1. **Start with the equations**:
- Equation 1: 2x - 9y = 14
- Equation 2: x = -6y + 7
2. **Substitute x from Equation 2 into Equation 1**:
Substitute x = -6y + 7 into Equation 1:
2(-6y + 7) - 9y = 14
3. **Expand and simplify**:
Distribute the 2 on the left side:
-12y + 14 - 9y = 14
4. **Combine like terms**:
Combine the y terms and constants:
-21y + 14 = 14
5. **Isolate the variable**:
Move the constant to the other side:
-21y = 0
6. **Solve for y**:
Divide by -21 to solve for y:
y = 0
7. **Substitute y back into Equation 2 to find x**:
Substitute y = 0 into x = -6y + 7:
x = -6(0) + 7
x = 7
So, the correct solution is:
x = 7
y = 0