6. MP Use Tools Determine the solution of the system of equations shown. State what strategy and tool you will use to answer the question, explain your choice, and then find the answer. $$ \left\{\begin{array}{l} y=x+1 \ y=-2 x+4 \end{array}\right. $$

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UpStudy AI · Accepted Answer

**Strategy and Tool:**  
I will use the substitution method to solve the system of equations. Since the first equation is already solved for $$ y $$ as $$ y = x + 1 $$, it can be directly substituted into the second equation. This method minimizes algebraic manipulation and efficiently finds the solution.

**Step-by-Step Solution:**

1. **Write down the equations:**  
   $$
   \begin{aligned}
   y &= x + 1 \quad \text{(Equation 1)} \
   y &= -2x + 4 \quad \text{(Equation 2)}
   \end{aligned}
   $$

2. **Substitute $$ y $$ from Equation 1 into Equation 2:**  
   Replace $$ y $$ in Equation 2 with $$ x + 1 $$:
   $$
   x + 1 = -2x + 4
   $$

3. **Solve for $$ x $$:**  
   Add $$ 2x $$ to both sides to get all $$ x $$ terms on one side:
   $$
   x + 2x + 1 = 4 \quad \Rightarrow \quad 3x + 1 = 4
   $$
   Subtract $$ 1 $$ from both sides:
   $$
   3x = 3
   $$
   Divide both sides by $$ 3 $$:
   $$
   x = 1
   $$

4. **Solve for $$ y $$:**  
   Substitute $$ x = 1 $$ back into Equation 1:
   $$
   y = 1 + 1 = 2
   $$

**Final Answer:**  
The solution to the system of equations is $$\boxed{x = 1, \, y = 2}$$.
The solution is $$ x = 1 $$ and $$ y = 2 $$.

MP Use Tools Determine the solution of the system of equations shown. State what strategy and tool you will use to answer the question, explain your choice, and then find the answer.

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