Question

What step can be taken to change the equation
3
4
​
x−
3
5
​
y=6 to standard form?

Multiply all terms by 3.

Multiply all terms by
3
1
​
.

None of these steps can be taken.

Multiply all terms by −3.

Answer 1

To change the equation \( \frac{3}{4}x - \frac{3}{5}y = 6 \) to standard form, we want to eliminate the fractions. A common way to do this is to find a common multiple of the denominators and multiply every term by that amount.

The denominators in this equation are 4 and 5. The least common multiple (LCM) of 4 and 5 is 20.

So, you would multiply every term in the equation by 20 to eliminate the fractions:

\[
20 \left( \frac{3}{4}x \right) - 20 \left( \frac{3}{5}y \right) = 20(6)
\]

This would give us:

\[
15x - 12y = 120
\]

Now, the options you've provided don't directly offer this approach, but let's analyze the options given:

1. Multiply all terms by 3.
2. Multiply all terms by \(\frac{3}{1}\).
3. None of these steps can be taken.
4. Multiply all terms by -3.

Multiplying by 3 or \(\frac{3}{1}\) would still leave fractions, and multiplying by -3 would change the signs but wouldn't eliminate fractions.

Therefore, the most appropriate answer based on the options provided is:

**None of these steps can be taken.**

However, if there's an option to multiply by 20 (or another number that specifically targets the denominators), that would be the correct approach.