Question
What step can be taken to change the equation
2
1
x+2y=12 to standard form?
Multiply all terms by −2.
Multiply all terms by
2
1
.
Multiply all terms by 2.
None of these steps can be taken.
2
1
x+2y=12 to standard form?
Multiply all terms by −2.
Multiply all terms by
2
1
.
Multiply all terms by 2.
None of these steps can be taken.
Answers
GPT-4o mini
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.**
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.**