Step by step
The question
Question: solve x = 3y − 2 and 2x + y = 10.
We call them ① and ②.
We want the x and y that make both true.
1 Put ① into ②
In ①, x is already alone.
x is the same as 3y − 2.
So in ②, we write (3y − 2) in place of x.
The brackets keep it together.
Putting one thing in place of another is called substitution.
2 Find y
The 2 in front of the bracket multiplies every part inside.
So we write 2 times each part.
Careful!
Not only the first part!
−2 is multiplied by 2 too.
Work out each multiplication.
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the y terms go together.
6y + y = 7y.
Now we have 7y − 4 = 10.
We want y by itself.
The − 4 is in the way.
To remove − 4, we add 4.
We do it on both sides, so they stay equal.
− 4 and + 4 make zero.
Cross them out.
10 plus 4 is 14.
Now we have 7y = 14.
7y means 7 times y.
We want just y.
To remove times 7, we divide by 7.
We do it on both sides, so they stay equal.
7 divided by 7 is 1.
So just y is left.
14 divided by 7 is 2.
So y = 2.
3 Find x
Now we put y = 2 into ①.
That is 6 − 2.
So x = 4.
So x = 4 and y = 2, both at the same time.
We write it as (4, 2).
On a graph, it is the point where the two lines meet.
4 Check
Let's check in both equations.
We put x = 4 and y = 2 into ①.
And the right side.
Both sides are 4.
Now ②.
We get 10, the same as the right side.
Both work.
So the answer is right!
Let's look back.
First: put ① into ②.
Then: find y.
Then: find x.
Last: check.