https://file.aiquickdraw.com/mathbot/file/1729186703393oytm1w1v.jpg

To solve the system of equations:

\[
\begin{aligned}
x + 2y &= 4 \\
4x + 5y &= 7
\end{aligned}
\]

### Step 1: Solve one equation for one variable
From the first equation \( x + 2y = 4 \), solve for \( x \):

\[
x = 4 - 2y
\]

### Step 2: Substitute into the second equation
Substitute \( x = 4 - 2y \) into the second equation \( 4x + 5y = 7 \):

\[
4(4 - 2y) + 5y = 7
\]
Simplify:

\[
16 - 8y + 5y = 7
\]
\[
16 - 3y = 7
\]
Solve for \( y \):

\[
-3y = 7 - 16
\]
\[
-3y = -9
\]
\[
y = 3
\]

### Step 3: Substitute \( y = 3 \) back into the first equation
Substitute \( y = 3 \) into \( x = 4 - 2y \):

\[
x = 4 - 2(3)
\]
\[
x = 4 - 6
\]
\[
x = -2
\]

### Solution:
\[
x = -2, \quad y = 3
\]

Let me know if you want further details or explanations.

Here are some related questions:
1. What method would you use to solve a system with three equations?
2. Can the substitution method always be used for nonlinear systems?
3. How can you check if a system of equations has no solution or infinite solutions?
4. What are the advantages of using elimination over substitution?
5. How would you graphically represent this system of equations?

**Tip**: Always check your solution by substituting both values back into the original equations to ensure they satisfy both.

Solve the system of equations: x + 2y = 4, 4x + 5y = 7

Learn how to solve the system of linear equations x + 2y = 4 and 4x + 5y = 7 using the substitution method. This step-by-step solution covers key algebraic concepts and is suitable for students in Grades 8-10.

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