Step by step
The question
Question: solve y = −x + 4 and 2x − y = 5.
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 + 4.
So in ②, we write (−x + 4) in place of y.
The brackets keep it together.
Putting one thing in place of another is called substitution.
2 Find x
A minus in front of a bracket changes the sign of every part inside.
Careful!
Not only the first sign!
The sign of 4 changes too.
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 − 4 = 5.
We want x 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.
5 plus 4 is 9.
Now we have 3x = 9.
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.
9 divided by 3 is 3.
So x = 3.
3 Find y
Now we put x = 3 into ①.
So y = 1.
So x = 3 and y = 1, both at the same time.
We write it as (3, 1).
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 = 1 into ①.
And the right side.
Both sides are 1.
Now ②.
We get 5, 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.