We are given the system of linear equations:

1. \( 2x + 5y = 37 \)
2. \( 4x + 3y = 39 \)

We can solve this system using either substitution or elimination. Let's use the **elimination method**.

### Step 1: Eliminate one variable
First, we'll multiply both sides of the first equation by 2 so that the coefficients of \( x \) in both equations will match:

\[
2(2x + 5y) = 2(37)
\]

\[
4x + 10y = 74
\]

Now, we have:
- \( 4x + 10y = 74 \)
- \( 4x + 3y = 39 \)

### Step 2: Subtract the second equation from the first
\[
(4x + 10y) - (4x + 3y) = 74 - 39
\]

\[
7y = 35
\]

### Step 3: Solve for \( y \)
\[
y = \frac{35}{7} = 5
\]

### Step 4: Substitute \( y = 5 \) into one of the original equations
We'll substitute \( y = 5 \) into the first equation:

\[
2x + 5(5) = 37
\]

\[
2x + 25 = 37
\]

\[
2x = 37 - 25
\]

\[
2x = 12
\]

\[
x = \frac{12}{2} = 6
\]

### Final Solution:
- \( x = 6 \)
- \( y = 5 \)

Do you want more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How can we verify the solution to a system of linear equations?
2. What are the other methods to solve systems of equations?
3. How do we determine if a system of equations has one solution, no solution, or infinitely many solutions?
4. Can elimination work in all cases of solving linear systems?
5. How does the substitution method differ from the elimination method?

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

Learn how to solve the system of linear equations 2x + 5y = 37 and 4x + 3y = 39 using the elimination method. This step-by-step solution covers algebraic concepts, properties of equality, and practical techniques for solving linear equations. Suitable for students in Grades 8-10.

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