To solve the system of equations using the elimination method, we have the following equations:

1. \( 3x + 4y = -25 \)
2. \( 2x - 3y = 6 \)

### Step 1: Eliminate one variable.
We aim to eliminate one variable by making the coefficients of either \(x\) or \(y\) the same. Let's eliminate \(x\) by finding a common multiple of the coefficients of \(x\) in both equations. The least common multiple of 3 and 2 is 6. 

Multiply both equations by factors that will give us the same coefficient for \(x\):

- Multiply the first equation by 2:
  \[
  2(3x + 4y) = 2(-25) \implies 6x + 8y = -50
  \]
- Multiply the second equation by 3:
  \[
  3(2x - 3y) = 3(6) \implies 6x - 9y = 18
  \]

Now we have the system:
\[
6x + 8y = -50
\]
\[
6x - 9y = 18
\]

### Step 2: Subtract the equations to eliminate \(x\).
Now subtract the second equation from the first:
\[
(6x + 8y) - (6x - 9y) = -50 - 18
\]
\[
6x - 6x + 8y + 9y = -50 - 18
\]
\[
17y = -68
\]

### Step 3: Solve for \(y\).
\[
y = \frac{-68}{17} = -4
\]

### Step 4: Substitute \(y = -4\) into one of the original equations.
We can use the first equation:
\[
3x + 4(-4) = -25
\]
\[
3x - 16 = -25
\]
\[
3x = -25 + 16
\]
\[
3x = -9
\]
\[
x = \frac{-9}{3} = -3
\]

### Final Solution:
The solution to the system is:
\[
x = -3, \quad y = -4
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you solve the system if substitution was used instead of elimination?
2. What happens if both equations in a system are identical?
3. Can a system of equations have no solution? If yes, under what conditions?
4. What if both variables are eliminated and you're left with a true statement?
5. How do you graphically represent the solution to a system of linear equations?

**Tip**: When using elimination, always check that your coefficients for the variable you want to eliminate match before subtracting the equations!

elimination 3x + 4y = -25 and 2x - 3y = 6

Discover how to solve the system of linear equations 3x + 4y = -25 and 2x - 3y = 6 using the elimination method. Follow the detailed steps, including eliminating variables and solving for x and y. Suitable for students in Grades 9-11.

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