To solve the system of equations:

1. \( 3x - 5y = 9 \)
2. \( 2x + 3y = 25 \)

we can use the elimination or substitution method. Here, I’ll use the elimination method to eliminate \( y \) and solve for \( x \).

### Step 1: Make the coefficients of \( y \) the same
Multiply the first equation by 3 and the second equation by 5 to make the \( y \)-terms equal in magnitude:

\[
3(3x - 5y) = 3 \cdot 9
\]
\[
5(2x + 3y) = 5 \cdot 25
\]

This results in:
1. \( 9x - 15y = 27 \)
2. \( 10x + 15y = 125 \)

### Step 2: Add the equations to eliminate \( y \)

Adding the two equations:

\[
(9x - 15y) + (10x + 15y) = 27 + 125
\]

This simplifies to:

\[
19x = 152
\]

### Step 3: Solve for \( x \)

\[
x = \frac{152}{19} = 8
\]

### Step 4: Substitute \( x = 8 \) back into one of the original equations to find \( y \)

Using the first equation:
\[
3(8) - 5y = 9
\]
\[
24 - 5y = 9
\]
\[
-5y = 9 - 24
\]
\[
-5y = -15
\]
\[
y = 3
\]

### Solution
The solution to the system is:
\[
x = 8, \quad y = 3
\]

Would you like further details, or do you have any questions about this solution?

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Here are 5 related questions to expand on this information:

1. How would you solve this system using the substitution method?
2. What would happen if both equations in the system were parallel?
3. Can you solve a similar system with three variables?
4. What does the solution \((x, y) = (8, 3)\) represent graphically?
5. How can you check if a solution to a system of equations is correct?

**Tip:** Always double-check your solution by substituting back into the original equations.

Explore how to solve the system of linear equations 3x - 5y = 9 and 2x + 3y = 25 using the elimination method. This detailed guide walks through aligning terms, eliminating variables, and finding values for x and y. Ideal for students in Grades 8-10.

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