Let's solve the system of equations step by step.

You provided two equations:

1. \( 2x - 3y = 10 \)
2. \( -2x + 3 = -10 \)

### Step 1: Simplify the second equation
First, simplify the second equation:

\[
-2x + 3 = -10
\]

Subtract 3 from both sides:

\[
-2x = -10 - 3
\]

\[
-2x = -13
\]

Divide by -2:

\[
x = \frac{13}{2}
\]

### Step 2: Substitute \( x = \frac{13}{2} \) into the first equation
Now substitute \( x = \frac{13}{2} \) into the first equation:

\[
2\left(\frac{13}{2}\right) - 3y = 10
\]

This simplifies to:

\[
13 - 3y = 10
\]

### Step 3: Solve for \( y \)
Subtract 13 from both sides:

\[
-3y = 10 - 13
\]

\[
-3y = -3
\]

Divide by -3:

\[
y = 1
\]

### Final Solution:
The solution to the system of equations is:

\[
x = \frac{13}{2}, \quad y = 1
\]

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do you solve a system of equations using substitution?
2. What are other methods to solve a system of linear equations?
3. How do you graphically represent the solution to this system?
4. What does it mean if a system of equations has no solution or infinite solutions?
5. How can you verify the solution to a system of equations?

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

Learn how to solve the system of equations 2x - 3y = 10 and -2x + 3 = -10 with a detailed step-by-step solution. This problem covers linear equations and the substitution method. Suitable for students in Grades 7-9.

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