Katarina's given equation is:
[tex]\[ 4x - \frac{2}{3}y = 8 \][/tex]
Sofiya advised Katarina to transform this equation into its standard form. The standard form of a linear equation [tex]\(Ax + By = C\)[/tex] requires the coefficients to be integers and there should be no fractions involved. Let's take this step by step to see the correct procedure and end result.
1. Clear the Fraction:
Multiply both sides of the equation by 3 to eliminate the fraction:
[tex]\[ 3 \cdot \left(4x - \frac{2}{3}y\right) = 3 \cdot 8 \][/tex]
Simplifying inside the parentheses:
[tex]\[ 3 \cdot 4x - 3 \cdot \frac{2}{3}y = 24 \][/tex]
Which gives:
[tex]\[ 12x - 2y = 24 \][/tex]
2. Simplified Further (if needed):
Now, divide both sides of the equation by 2 to simplify the coefficients:
[tex]\[ \frac{12x - 2y}{2} = \frac{24}{2} \][/tex]
Simplifying gives:
[tex]\[ 6x - y = 12 \][/tex]
Thus, Sofiya's advice was to "Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is [tex]\(6x - y = 12\)[/tex]."
So the correct advice Sofiya gave corresponds to:
Option 2: Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is [tex]\(6x - y = 12\)[/tex].
