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: $(-1,4)$

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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: $(-5,5)$

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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! 🎯