Math CentralQuandaries & Queries


Question from Sara, a student:

Rewrite the following equation:
in function form ("solve for y").

Also, please explain how to solve the problem. Thanks!!!

Hi Sara,

let me illustrate with 5x + 15y = 70.

The task is to manipulate the equation, always keeping the two sides equal, and end with an equation of the form

y = some expression that doesn't contain the letter y.

There are four operations I can perform and still maintain the equality of the two sides of the equation.

  • I can add the same amount to each side

  • I can subtract the same amount to each side.

  • I can multiply each side by the same amount.

  • I can divide each side by the same amount, as long as I don't divide by zero. Division by zero is never a legitimate operation.

Looking at the equation I notice that each of the numbers is divisible by 5 so I can divide each side by 5 to obtain

5x + 15y = 70
(5x + 15y)/5 = 70/5
5x/5 + 15y/5 = 14
x + 3y = 14

I don't want the x on the left side of the equation so subtract x from each side.

x + 3y = 14
x + 3y - x = 14 - x
3y = 14 - x

Almost there. Finally divide each side by 3.

3y = 14 - x
3y/3 = (14 - x)/3
y = 14/3 - x/3

Now try your problem,

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