Make x the subject of xy + 3 = 2x + y

Step by step

The question

Question: make x the subject of xy + 3 = 2x + y.

The subject is the letter on its own: we want x = ...

.

Here x is in two places, so we must bring them together.

1 Get the x terms on one side

2x is on the right.

To remove it, we take away 2x.

We do it on both sides, so they stay equal.

Careful!

A term that moves to the other side changes its sign.

2x becomes −2x.

2x and −2x make zero.

Cross them out.

Now we have xy + 3 − 2x = y.

3 has no x.

To remove it from the left, we take away 3.

We do it on both sides, so they stay equal.

3 and −3 make zero.

Cross them out.

Now both x terms are on the left: xy − 2x = y − 3.

2 Take x out

x is in every part.

So we take it out once, and write what is left in a bracket.

So x times (y − 2) is y − 3.

3 Remove the (y − 2)

(y − 2)x means (y − 2) times x.

We want just x.

To remove times (y − 2), we divide by (y − 2).

We do it on both sides.

(y − 2) divided by (y − 2) is 1.

So just x is left.

So x = (y − 3)/(y − 2).

4 Check

Let's check with numbers.

We pick y = 4.

Our answer gives x = 1/2.

Now we put all the numbers into the start.

First the left side.

Now the right side.

Both sides are 1.

So our answer is right!

Let's look back.

First: get the x terms on one side.

Then: take x out.

Then: remove the (y − 2).

Last: check.