5x-2y=-5                                                                                                                                                                                   5x+6y=35

You are solving the system of equations:

1. \( 5x - 2y = -5 \)
2. \( 5x + 6y = 35 \)

To solve this system, we can use either substitution or elimination. Here, I will use the **elimination method** to eliminate \( x \) and solve for \( y \).

### Step 1: Eliminate \( x \)

Subtract equation (1) from equation (2):

\[
(5x + 6y) - (5x - 2y) = 35 - (-5)
\]

Simplifying:

\[
5x + 6y - 5x + 2y = 35 + 5
\]

\[
8y = 40
\]

Solve for \( y \):

\[
y = \frac{40}{8} = 5
\]

### Step 2: Substitute \( y = 5 \) into one of the original equations

Using the first equation:

\[
5x - 2(5) = -5
\]

\[
5x - 10 = -5
\]

Add 10 to both sides:

\[
5x = 5
\]

Solve for \( x \):

\[
x = \frac{5}{5} = 1
\]

### Final Solution:
\[
x = 1, \quad y = 5
\]

Would you like more details or clarifications on any part of the solution?

Here are 5 related questions for practice:
1. Solve the system: \( 3x - 4y = 7 \) and \( 2x + 5y = -1 \).
2. What happens if both equations in the system are parallel?
3. Solve using substitution: \( x + y = 10 \) and \( 2x - y = 4 \).
4. How can you graphically solve a system of equations?
5. What are the possible types of solutions for a system of linear equations?

**Tip:** The elimination method is very efficient when the coefficients of one variable are already the same or easily made equal!

Learn how to solve the system of linear equations 5x - 2y = -5 and 5x + 6y = 35 using the elimination method. This detailed solution covers essential algebraic concepts and formulas, perfect for students in Grades 8-10.

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