https://file.aiquickdraw.com/mathbot/file/1725285458037oogp4lx3.jpg

To solve the system of equations using the substitution method, let's start by writing down the equations from the image:

\[
\begin{aligned}
1. & \quad x + 2y = 4 \\
2. & \quad y = 3 - x
\end{aligned}
\]

### Step 1: Substitute the expression for \( y \) from the second equation into the first equation.

Substitute \( y = 3 - x \) into the first equation:

\[
x + 2(3 - x) = 4
\]

### Step 2: Simplify and solve for \( x \).

Expand and simplify the equation:

\[
x + 6 - 2x = 4
\]

Combine like terms:

\[
-x + 6 = 4
\]

Subtract 6 from both sides:

\[
-x = -2
\]

Multiply both sides by -1:

\[
x = 2
\]

### Step 3: Substitute the value of \( x \) back into the second equation to find \( y \).

Now substitute \( x = 2 \) into the second equation:

\[
y = 3 - 2
\]

Simplify:

\[
y = 1
\]

### Solution:
The solution to the system of equations is \( x = 2 \) and \( y = 1 \).

Would you like more details or have any questions? Here are some related questions that might interest you:

1. How does the substitution method compare to the elimination method?
2. What are some situations where the substitution method is preferred?
3. Can you explain the geometric interpretation of solving this system of equations?
4. How would you solve this system using matrix methods?
5. What if the system of equations was non-linear? How would the substitution method change?

**Tip:** Always check your solution by substituting the values back into the original equations to verify correctness.

Learn how to solve a system of equations using the substitution method with a step-by-step guide. This problem involves substituting variables to find solutions. Suitable for high school students.

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