Question

The graph of the system of equations is given below:
Red Line: y=3+2

Blue Line: y=-x+6
Part II: Use the substitution method to solve the system of equations. Show ALL work. Write your final answer as an ordered pair
.x,y

Answer 1

To solve the system of equations using the substitution method, we first define the two equations based on the given descriptions:

1. Red Line: \( y = 3 + 2 \) simplifies to \( y = 5 \).
2. Blue Line: \( y = -x + 6 \).

Now we have the following system of equations:
\[
y = 5
\]
\[
y = -x + 6
\]

Next, we'll use the first equation \( y = 5 \) to substitute for \( y \) in the second equation.

**Step 1: Substitute \( y \) in the second equation**
\[
5 = -x + 6
\]

**Step 2: Solve for \( x \)**
To isolate \( x \), we can subtract 6 from both sides:
\[
5 - 6 = -x
\]
\[
-1 = -x
\]

Multiplying both sides by -1 gives us:
\[
x = 1
\]

**Step 3: Find \( y \) using the value of \( x \)**
Now that we have \( x = 1 \), we'll substitute this value back into the first equation to find \( y \):
\[
y = 5
\]

**Final Answer:**
The solution to the system of equations is:
\[
\boxed{(1, 5)}
\]

This is the ordered pair solution of the system.