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The given system of simultaneous equations is:

\[
1) \ 2x + 3y = 6
\]
\[
2) \ 3x - 2y = 22
\]

### Solving the system of equations:

#### Step 1: Multiply the equations to eliminate one variable
We can eliminate \(y\) by multiplying the first equation by 2 and the second equation by 3:

\[
1) \ 4x + 6y = 12
\]
\[
2) \ 9x - 6y = 66
\]

#### Step 2: Add the two equations
Adding both equations together eliminates \(y\):

\[
(4x + 6y) + (9x - 6y) = 12 + 66
\]
\[
13x = 78
\]

#### Step 3: Solve for \(x\)
\[
x = \frac{78}{13} = 6
\]

#### Step 4: Substitute \(x = 6\) into one of the original equations
We substitute into the first equation:
\[
2(6) + 3y = 6
\]
\[
12 + 3y = 6
\]
\[
3y = 6 - 12
\]
\[
3y = -6 \quad \Rightarrow \quad y = \frac{-6}{3} = -2
\]

### Final Solution:
The solution to the system of equations is:
\[
x = 6, \quad y = -2
\]

Would you like further clarification on any step?

Here are 5 related questions to explore further:
1. What methods can be used to solve systems of equations other than elimination?
2. How would you solve the system if it involved fractions?
3. Can substitution be used to solve the same system of equations? How?
4. What is the geometric interpretation of solving two simultaneous equations?
5. How do we identify whether a system of equations has no solution or infinitely many solutions?

**Tip:** When solving simultaneous equations, ensure that you're clear on which variable you aim to eliminate first for a smoother process!

Solve the simultaneous equations: 2x + 3y = 6 and 3x - 2y = 22.

Learn how to solve the system of linear equations: 2x + 3y = 6 and 3x - 2y = 22 using the method of elimination. This problem covers key algebraic concepts such as simultaneous equations and linear equations. Suitable for students in Grades 8-10.

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