https://file.aiquickdraw.com/mathbot/file/17272541082718eg00ddd.jpg

You provided the system of equations from the image:

\[
\begin{aligned}
1) & \ \ 2x - 3y = 7 \\
2) & \ \ 2y - 3x = -8
\end{aligned}
\]

I will solve this system of equations using substitution or elimination method.

### Step 1: Rewriting the equations:
Let's rewrite the second equation for clarity:
\[
-3x + 2y = -8
\]

Now we have the system:

\[
\begin{aligned}
1) & \ \ 2x - 3y = 7 \\
2) & \ \ -3x + 2y = -8
\end{aligned}
\]

### Step 2: Multiply both equations to align coefficients
We can use the elimination method by multiplying both equations to make the coefficients of \(x\) or \(y\) equal. To eliminate \(x\), multiply the first equation by 3 and the second by 2:

\[
3(2x - 3y) = 3(7) \quad \Rightarrow \quad 6x - 9y = 21
\]
\[
2(-3x + 2y) = 2(-8) \quad \Rightarrow \quad -6x + 4y = -16
\]

### Step 3: Add the two equations to eliminate \(x\):
\[
(6x - 9y) + (-6x + 4y) = 21 + (-16)
\]
\[
-5y = 5
\]
### Step 4: Solve for \(y\):
\[
y = \frac{5}{-5} = -1
\]

### Step 5: Substitute \(y = -1\) into one of the original equations:
Substitute into the first equation:
\[
2x - 3(-1) = 7
\]
\[
2x + 3 = 7
\]
\[
2x = 7 - 3 = 4
\]
\[
x = \frac{4}{2} = 2
\]

### Final Answer:
The solution to the system of equations is:
\[
x = 2, \quad y = -1
\]

Would you like further details or have any questions? 

Here are 5 related questions for practice:
1. Can you solve a similar system of equations with different coefficients?
2. What happens if the system of equations has no solution?
3. How would you solve a system using the substitution method?
4. Can you solve a system where both variables are in terms of fractions?
5. How would you solve this system graphically?

**Tip**: Always verify your solution by substituting the values of \(x\) and \(y\) back into the original equations!

Learn how to solve the system of equations 2x - 3y = 7 and 2y - 3x = -8 using the elimination method. This problem covers key algebraic concepts and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation