Question

-2/3x+y=-4 standard form

Answer 1

To convert the equation \(-\frac{2}{3}x + y = -4\) into standard form, we want to express it in the form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers and \(A\) is non-negative.

Starting from the given equation:

\[
-\frac{2}{3}x + y = -4
\]

1. First, we can eliminate the fraction by multiplying every term by 3 (the denominator):

\[
3 \left(-\frac{2}{3}x\right) + 3y = 3(-4)
\]

This simplifies to:

\[
-2x + 3y = -12
\]

2. To ensure \(A\) is non-negative, we can multiply the entire equation by -1:

\[
2x - 3y = 12
\]

Now, the equation is in standard form, where \(A = 2\), \(B = -3\), and \(C = 12\):

\[
2x - 3y = 12
\]