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1. If 2x - 3y = 6, then 6y - 4x = ?
- A. -12
- B. -12
- C. -12
- D. -12
Answer: Option A
Explanation:
To find the value of 6y - 4x when 2x - 3y = 6, you can rearrange the first equation to isolate 2x:
2x = 6 + 3y
Now, divide both sides by 2:
x = 3 + (3/2)y
Now, you can use this expression for x to find 6y - 4x:
6y - 4x = 6y - 4(3 + (3/2)y)
Now, distribute the -4 on the right side:
6y - 4x = 6y - 12 - 6y
Now, you can see that the 6y terms cancel out:
6y - 4x = -12
So, 6y - 4x equals -12.
2x = 6 + 3y
Now, divide both sides by 2:
x = 3 + (3/2)y
Now, you can use this expression for x to find 6y - 4x:
6y - 4x = 6y - 4(3 + (3/2)y)
Now, distribute the -4 on the right side:
6y - 4x = 6y - 12 - 6y
Now, you can see that the 6y terms cancel out:
6y - 4x = -12
So, 6y - 4x equals -12.
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