Question
What step can be taken to change the equation −2x+
4
3
y=6 to standard form?
Multiply all terms by 2.
None of these steps can be taken.
Multiply all terms by 3.
Multiply all terms by
2
1
.
4
3
y=6 to standard form?
Multiply all terms by 2.
None of these steps can be taken.
Multiply all terms by 3.
Multiply all terms by
2
1
.
Answers
GPT-4o mini
To change the equation \(-2x + \frac{4}{3}y = 6\) to standard form, you typically want to eliminate any fractions and have the equation in the form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers.
To eliminate the fraction \(\frac{4}{3}y\), you could multiply the entire equation by 3, which is the denominator of the fraction:
\[
3 \left(-2x\right) + 3 \left(\frac{4}{3}y\right) = 3(6)
\]
This simplifies to:
\[
-6x + 4y = 18
\]
Now, the equation is in standard form, which is \(Ax + By = C\).
So, the correct step to take is:
**Multiply all terms by 3.**
To eliminate the fraction \(\frac{4}{3}y\), you could multiply the entire equation by 3, which is the denominator of the fraction:
\[
3 \left(-2x\right) + 3 \left(\frac{4}{3}y\right) = 3(6)
\]
This simplifies to:
\[
-6x + 4y = 18
\]
Now, the equation is in standard form, which is \(Ax + By = C\).
So, the correct step to take is:
**Multiply all terms by 3.**