What is the result of solving this equation for x?

Question

ax+by=c

A. x=c-by/a


B. x=a(c-by)

C. x=a(c+by)

D. x=c+by/a

Answer 1

To solve the equation \( ax + by = c \) for \( x \), we need to isolate \( x \).

1. Start with the original equation: \[ ax + by = c \]

2. Subtract \( by \) from both sides: \[ ax = c - by \]

3. Finally, divide both sides by \( a \) (assuming \( a \neq 0 \)): \[ x = \frac{c - by}{a} \]

This can also be written as: \[ x = \frac{c}{a} - \frac{by}{a} \]

Now, let's compare this with the choices provided:

A. \( x = \frac{c - by}{a} \) - This matches our final equation.

B. \( x = a(c - by) \)

C. \( x = a(c + by) \)

D. \( x = \frac{c + by}{a} \)

The correct answer is:

A. \( x = \frac{c - by}{a} \)