Step by step
The question
Question: solve y = 2x + 1 and 3x + y = 11.
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 2x + 1.
So in ②, we write (2x + 1) 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.
3x + 2x = 5x.
Now we have 5x + 1 = 11.
We want x by itself.
The + 1 is in the way.
To remove + 1, we take away 1.
We do it on both sides, so they stay equal.
+ 1 and − 1 make zero.
Cross them out.
11 minus 1 is 10.
Now we have 5x = 10.
5x means 5 times x.
We want just x.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
So just x is left.
10 divided by 5 is 2.
So x = 2.
3 Find y
Now we put x = 2 into ①.
That is 4 + 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 11, 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.