Solve y = 3x - 5, y = x + 1

Step by step

The question

Question: solve y = 3x − 5 and y = x + 1.

We call them ① and ②.

We want the x and y that make both true.

1 Put ① into ②

In ①, y is already alone.

y is the same as 3x − 5.

So in ②, we write (3x − 5) in place of y.

The brackets keep it together.

Putting one thing in place of another is called substitution.

2 Find x

A bracket with a plus or nothing in front can just be removed.

There is x on both sides.

We want x on one side only.

So we take away x on both sides.

x and − x make zero.

Cross them out.

3x minus x is 2x.

Now we have 2x − 5 = 1.

We want x by itself.

The − 5 is in the way.

To remove − 5, we add 5.

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

− 5 and + 5 make zero.

Cross them out.

1 plus 5 is 6.

Now we have 2x = 6.

2x means 2 times x.

We want just x.

To remove times 2, we divide by 2.

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

2 divided by 2 is 1.

So just x is left.

6 divided by 2 is 3.

So x = 3.

3 Find y

Now we put x = 3 into ①.

That is 9 − 5.

So y = 4.

So x = 3 and y = 4, both at the same time.

We write it as (3, 4).

On a graph, it is the point where the two lines meet.

4 Check

Let's check in both equations.

We put x = 3 and y = 4 into ①.

And the right side.

Both sides are 4.

Now ②.

And the right side.

Both sides are 4.

Both work.

So the answer is right!

Let's look back.

First: put ① into ②.

Then: find x.

Then: find y.

Last: check.