Question

solve the equation for x.
ax + by = c
\\( x = a(c + by) \\)
\\( x = a(c - by) \\)
\\( x = \frac{c - by}{a} \\)
\\( x = \frac{c + by}{a} \\)

Explanation:

Step1: Isolate the term with x

We start with the equation \( Ax + By = C \). To isolate the term containing \( x \), we subtract \( By \) from both sides of the equation.

$$ Ax + By - By = C - By $$

Simplifying the left side (since \( By - By = 0 \)), we get:

$$ Ax = C - By $$

Step2: Solve for x

Now, to solve for \( x \), we divide both sides of the equation \( Ax = C - By \) by \( A \) (assuming \( A
eq0 \)).

$$ \frac{Ax}{A}=\frac{C - By}{A} $$

Simplifying the left side (since \( \frac{Ax}{A}=x \) when \( A
eq0 \)), we obtain:

$$ x=\frac{C - By}{A} $$

Answer:

\( x = \frac{C - By}{A} \) (corresponding to the option \( x=\frac{C - By}{A} \) among the given choices)