\( \begin{array}{l}y=7-x \\ x+2 y=12\end{array} \) (1)) What is one way you can use substitution to solve this problem? (1)) Substitute \( 7-x \) for \( y \) \( \left(\begin{array}{l}\text { (1) }\end{array}\right. \) Now, find the solution to the system of equations,

To solve the system of equations using substitution, we can follow these steps: 1. **Identify the equations:** \[ \begin{array}{l} y = 7 - x \quad \text{(Equation 1)} \\ x + 2y = 12 \quad \text{(Equation 2)} \end{array} \] 2. **Substitute \( y \) in Equation 2:** We will substitute \( 7 - x \) for \( y \) in Equation 2. So, Equation 2 becomes: \[ x + 2(7 - x) = 12 \] 3. **Simplify the equation:** Now, we will simplify the equation: \[ x + 14 - 2x = 12 \] Combine like terms: \[ -x + 14 = 12 \] 4. **Solve for \( x \):** Subtract 14 from both sides: \[ -x = 12 - 14 \] \[ -x = -2 \] Multiply by -1: \[ x = 2 \] 5. **Substitute \( x \) back to find \( y \):** Now that we have \( x = 2 \), we can substitute it back into Equation 1 to find \( y \): \[ y = 7 - x = 7 - 2 = 5 \] 6. **Final solution:** The solution to the system of equations is: \[ (x, y) = (2, 5) \] Thus, the solution to the system of equations is \( (2, 5) \).