Question

Solve the formula for the variable y: 5x+2y=10

Answer 1

The process is to go step-by-step to isolate the y.

To do this, you basically run the order of operations in reverse.

In 5x+2y=10, the first thing to move away from the left side is 5x and  you cancel it out by subtracting 5x from both sides:

    5x+2y - 5x = 10 - 5x

The 5x's on the left cancel leaving you with:  

   2y = 10 - 5x

Side note: this is more commonly written as 2y = -5x+10, since we tend to write variable terms first.

Finally, to get the y fully by itself, you need to cancel the 2 that's multplied against it.  To cancel multiplication, you need to divide:

    $\dfrac{2y}{2} = \dfrac{-5x+10}{2}$

The most important thing to remember here is that the 2 needs to divide into both terms on the right:

    $\dfrac{2y}{2} = \dfrac{-5x}{2}+ \dfrac{10}{2}$

Finally, we simplify this into:

    $y = -\dfrac{5}{2}x+5$