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Bunuel
If 2x - 3y = 6, then 6y - 4x =

A. -12
B. -6
C. 6
D. 12
E. Cannot be determined


Given ,

2x - 3y = 6

6y - 4x = -12 ( multiply by -2 )

The best answer is A.
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Bunuel
If 2x - 3y = 6, then 6y - 4x =

A. -12
B. -6
C. 6
D. 12
E. Cannot be determined

6y - 4x = -2 (2x - 3y) = -2 * 6 =-12

Answer: A
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Bunuel
If 2x - 3y = 6, then 6y - 4x =

A. -12
B. -6
C. 6
D. 12
E. Cannot be determined

Multiplying the given equation by -2, we have:

-4x + 6y = 6y - 4x = -12

Answer: A
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The trick here is to notice that 6y - 4x is just the expression 2x - 3y multiplied by -2.

Let me show you step by step:

Step 1: We're given: 2x - 3y = 6

Step 2: We need to find: 6y - 4x

Step 3: Now, multiply both sides of the given equation by -2:

-2 × (2x - 3y) = -2 × 6

Distribute the -2 on the left side:
(-2 × 2x) + (-2 × -3y) = -12
-4x + 6y = -12

Rearrange:
6y - 4x = -12

Answer: A

The most common mistake here is picking E (Cannot be determined), thinking you need individual values of x and y. You don't! The question only asks for the value of the entire expression 6y - 4x, not for x or y separately.

General principle: When a problem gives you one equation and asks for the value of a different expression, always check if the expression you need is just a multiple of the equation you were given. Multiply or divide the entire equation to match what's being asked.
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