Which of the following equations is equivalent to (1/2)x - (2/3)y = 5? 1. x - 2y = 10 2. 4x - 6y = 30 3. 3x - 4y = 30

Mathematics · College · Thu Feb 04 2021

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To determine which of the given equations is equivalent to the original equation

1/2x - 2/3y = 5, we need to manipulate the original equation to bring it to the same form as the given options, without changing the solutions that the equation represents.

We can start by finding a common denominator for the fractions in the equation to eliminate the fractions. The denominators are 2 and 3, so the least common multiple is 6. We multiply through by 6 to clear the fractions:

6 * (1/2x) - 6 * (2/3y) = 6 * 5

This simplifies to:

3x - 4y = 30

Now our modified equation matches one of the given options:

3x - 4y = 30

So, the equivalent equation is the third option.

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