Rearranging Algebraic Equations Question 1

The equation below shows the relationship between positive numbers $a$ , $b$ , $x$ , $y$ , and $c$ . Which of the following correctly expresses $a$ in terms of $b$ , $x$ , $y$ , and $c$ ? $ax+by=c$

a=c-\dfrac{x}{by}

a=c-\dfrac{by}{x}

a=\dfrac{c-by}{x}

a=\dfrac{c-x}{by}

Approach

If you have difficulties with these types of problem, try replacing variables with numbers and anticipating the steps you would normally use.

With variables

ax+by=c

ax=c-by

\boxed{x=\frac{c-by}{x}}

With numbers

a(1)+(2)(3)=(4)

a(1)=(4)-(2)(3)

a=\frac{(4)-(2)(3)}{(1)}

Sidenote

Did this question seem familiar? You've probably done a similar rearrangement many times before, when changing a line in standard form to slope-intercept form:

5x+3y=6

3y=-5x+6

y=-\frac{5}{3}x+2