Question

What step can be taken to change the equation −
5
4
​
x+
5
3
​
y=8 to standard form?

None of these steps can be taken.

Multiply all terms by −4.

Multiply all terms by −5.

Multiply all terms by 5.

Answer 1

To change the equation

\[
-\frac{5}{4}x + \frac{5}{3}y = 8
\]

to standard form, which is typically represented as \(Ax + By = C\) where \(A\), \(B\), and \(C\) are integers, we should eliminate the fractions.

1. The denominators in the equation are 4 and 3. To eliminate the fractions, we can find a common multiple of 4 and 3, which is 12.

2. We can multiply the entire equation by 12 to eliminate the fractions:

\[
12 \left(-\frac{5}{4}x\right) + 12 \left(\frac{5}{3}y\right) = 12 \cdot 8
\]

This results in:

\[
-15x + 20y = 96
\]

Now the equation is in standard form \(Ax + By = C\), where \(A = -15\), \(B = 20\), and \(C = 96\).

Among the options given, none of the direct multiplications by -4, -5, or 5 would yield the proper elimination of fractions. Therefore, the answer would be:

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

However, multiplying by 12 would be the best choice to convert the equation directly to its standard form.