-6x+2y=4x+y solve for x Give me some similar random problems the one I gave u generate 30

To solve the equation \(-6x + 2y = 4x + y\) for \(x\):

1. Start by moving all terms involving \(x\) to one side of the equation and all terms involving \(y\) to the other side:
   \[
   -6x - 4x = y - 2y
   \]
   Simplifying this gives:
   \[
   -10x = -y
   \]

2. Next, solve for \(x\) by dividing both sides of the equation by \(-10\):
   \[
   x = \frac{y}{10}
   \]

So, the solution is \(x = \frac{y}{10}\).

### Similar Problems:
Here are 30 random problems similar to the one you provided:

1. \(5x - 3y = -2x + 7y\)
2. \(4x + 6y = 3x - 2y\)
3. \(-8x + 2y = 4x - y\)
4. \(7x - y = -5x + 2y\)
5. \(-3x + 4y = 2x + 9y\)
6. \(2x - 5y = -4x + 3y\)
7. \(-9x + 7y = 5x - 2y\)
8. \(8x + y = -6x + 3y\)
9. \(-5x + 2y = 3x + 4y\)
10. \(3x - 6y = -x + y\)
11. \(-7x + 3y = 4x - 5y\)
12. \(6x - 2y = -3x + 7y\)
13. \(-4x + 5y = 2x - y\)
14. \(9x + 6y = -5x + 2y\)
15. \(-2x + y = 7x - 4y\)
16. \(5x - y = -6x + 3y\)
17. \(-6x + 7y = 2x - y\)
18. \(4x - 3y = -5x + 6y\)
19. \(-8x + y = 3x - 2y\)
20. \(7x + 4y = -9x + 2y\)
21. \(-3x - 2y = 6x + y\)
22. \(2x + 5y = -7x + 3y\)
23. \(-9x + y = 4x + 5y\)
24. \(8x - 3y = -2x + 7y\)
25. \(-5x + 6y = 3x - y\)
26. \(3x + 4y = -6x + 2y\)
27. \(-7x + y = 5x - 3y\)
28. \(6x + 5y = -8x + 2y\)
29. \(-4x - 3y = 2x + y\)
30. \(9x - y = -7x + 4y\)

Would you like more details on solving similar equations, or do you have any questions?

### Follow-Up Questions:
1. How do you handle solving equations with fractions?
2. What happens if the coefficients of \(x\) on both sides are equal?
3. How do you solve for \(y\) instead of \(x\) in these equations?
4. What if both \(x\) and \(y\) have the same coefficient?
5. How would you check the solution of a linear equation?

### Tip:
Always verify your solution by substituting it back into the original equation to ensure both sides are equal.

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