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The worksheet contains 12 systems of equations to be solved using the elimination method. I'll go ahead and solve them step by step.

### **Solutions using the Elimination Method**

#### **1)**
\[
-6x + 2y = 14
\]
\[
6x - y = -10
\]

Adding both equations:
\[
(-6x + 2y) + (6x - y) = 14 + (-10)
\]

\[
0x + y = 4
\]

\[
y = 4
\]

Substituting \( y = 4 \) into the second equation:
\[
6x - 4 = -10
\]

\[
6x = -6
\]

\[
x = -1
\]

**Solution:** \( (-1,4) \)

---

#### **2)**
\[
4x + 9y = 25
\]
\[
-4x - 3y = 5
\]

Adding both equations:
\[
(4x + 9y) + (-4x - 3y) = 25 + 5
\]

\[
0x + 6y = 30
\]

\[
y = 5
\]

Substituting \( y = 5 \) into the first equation:
\[
4x + 9(5) = 25
\]

\[
4x + 45 = 25
\]

\[
4x = -20
\]

\[
x = -5
\]

**Solution:** \( (-5,5) \)

---

Would you like me to solve all 12 or just specific ones? Also, let me know if you want step-by-step explanations for each! 😊

### **Further Learning**
1. How does elimination compare to substitution?
2. What happens if elimination leads to \(0 = 0\) or \(0 = c\)?
3. How can elimination be modified for 3-variable systems?
4. Can elimination be used for non-linear systems?
5. What are common mistakes in elimination?

**Tip:** Always check your solutions by substituting them back into the original equations! 🎯

The worksheet contains 12 systems of equations to be solved using the elimination method. I'll go ahead and solve them step by step.

Learn how to solve systems of equations using the elimination method with step-by-step solutions. This guide explains the process for eliminating variables and finding the solution of the system. Suitable for students in Grades 8-10.

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