(1) Use substitution to solve the system of equations. \( \begin{array}{l}x=3-2 y \\ 3 y=2 x+8 \\ \text { (1)) How can you use substitution in this problem? } \\ \text { (1) Substitute ? for ? }\end{array} \)

To solve the system of equations using **substitution**, follow these steps: \[ \begin{cases} x = 3 - 2y \quad \text{(Equation 1)} \\ 3y = 2x + 8 \quad \text{(Equation 2)} \end{cases} \] ### (1) How can you use substitution in this problem? **Substitution** involves solving one of the equations for one variable and then substituting that expression into the other equation. In this case: - **Equation 1** already solves for \( x \): \( x = 3 - 2y \). This allows us to substitute the expression for \( x \) from Equation 1 into Equation 2, eliminating \( x \) and allowing us to solve for \( y \). ### (2) Substitute ___ for ___. **Substitute \( 3 - 2y \) for \( x \).** Here's how it's done: 1. **Start with Equation 2:** \[ 3y = 2x + 8 \] 2. **Substitute \( x \) from Equation 1 into Equation 2:** \[ 3y = 2(3 - 2y) + 8 \] 3. **Now, solve for \( y \):** \[ 3y = 6 - 4y + 8 \\ 3y + 4y = 14 \\ 7y = 14 \\ y = 2 \] 4. **Find \( x \) using Equation 1:** \[ x = 3 - 2(2) \\ x = 3 - 4 \\ x = -1 \] **Solution:** \( x = -1 \) and \( y = 2 \). --- **Summary:** - **Use Substitution By:** Substituting \( 3 - 2y \) for \( x \) in the second equation. This method efficiently reduces the system to a single equation with one variable, making it easier to solve. **Answer:** Use substitution by replacing x with 3 – 2y. Specifically, substitute 3 − 2y for x in the second equation.