Step by step
The question
Question: solve y = x + 3 and 2x + y = 9.
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 x + 3.
So in ②, we write (x + 3) 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.
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
2x + x = 3x.
Now we have 3x + 3 = 9.
We want x by itself.
The + 3 is in the way.
To remove + 3, we take away 3.
We do it on both sides, so they stay equal.
+ 3 and − 3 make zero.
Cross them out.
9 minus 3 is 6.
Now we have 3x = 6.
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
6 divided by 3 is 2.
So x = 2.
3 Find y
Now we put x = 2 into ①.
So y = 5.
So x = 2 and y = 5, both at the same time.
We write it as (2, 5).
On a graph, it is the point where the two lines meet.
4 Check
Let's check in both equations.
We put x = 2 and y = 5 into ①.
And the right side.
Both sides are 5.
Now ②.
We get 9, the same as the right side.
Both work.
So the answer is right!
Let's look back.
First: put ① into ②.
Then: find x.
Then: find y.
Last: check.