What step can be taken to change the equation

Question

2
1
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x+2y=12 to standard form?

Multiply all terms by −2.

Multiply all terms by
2
1
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.

Multiply all terms by 2.

None of these steps can be taken.

Answer 1

To convert the equation \( \frac{1}{2}x + 2y = 12 \) to standard form, we want to eliminate any fractions.

Among the options provided, the correct step would be to multiply all terms by 2. Here’s how that would look:

1. Start with the original equation: \[ \frac{1}{2}x + 2y = 12 \]
2. Multiply every term by 2: \[ 2 \cdot \left(\frac{1}{2}x\right) + 2 \cdot (2y) = 2 \cdot 12 \] Which simplifies to: \[ x + 4y = 24 \]

Now the equation is in standard form \( Ax + By = C \).

So, the choice is: Multiply all terms by 2.