How do you change the subject of the formula?

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​All that changing the subject of the formula means is basically getting a letter on its own on one side of the equation. To begin, let's take a relatively simple example.

Make x the subject of the formula:

4y + 2 = x - 4 

What this question basically means is get x on its own. At the moment on the right hand side we have x - 4. So, because we want x on its own what we can do is add 4 to this side. However, we must then add 4 to the left hand side to balance the equation (remember what we do to one side when changing the subject of the formula WE MUST DO TO THE OTHER SIDE). This then gives us the following:

4y + 2 +4 = x

So our final answer is:

x = 4y + 6

We have successfully made x the subject of the formula. Now let's try something a little bit more challenging.

Make y the subject of the formula.

2y/5 - 3x = 2

First we must isolate the 2y/5. To do this we can add 3x to both sides to get rid of it on the left side and get 2y/5 on its own. This gives us:

2y/5 = 2 + 3x

Now, the 2y is divided by 5, therefore by doing the inverse function of division which is multiplication, we can get 2y on its own. So we can multiply both sides by 5.

2y/5 * 5 = 5 * (2 + 3x)

2y = 5(2 + 3x)

It's probably easier if these brackets are expand so:

2y = 10 + 15x

TIP: Remember to put brackets around 2 + 3x because both the 2 and the 3x are being multiplied by 5.

​Finally we must get y on its own. At the moment the y is being multiplied by 2. So we must do the inverse function and divide 2y by 2. Remember to divide by 2 on both sides.

2y / 2 = (10 + 15x) / 2

y = (10 + 15x) / 2

This can be simplified to:

y = 5 + 15x/2

This is because 10/2 = 5 and 15x2 =is just 15x/2.

We have now successfully made y the subject of the formula.

The key things to remember when changing the subject of the formula are:

 - All it means is get a letter on one side of the equation on its own

- Use inverses functions (+ and - are inverses of each other and so are * and /) to isolate the letter

​- Whatever you do to one side you must do to the other

Robbie T. GCSE Maths tutor, GCSE Geography tutor, GCSE Spanish tutor

About the author

is an online GCSE Maths tutor with MyTutor studying at Bristol University

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