Step by step
The question
Question: solve x + 2y = 4 and 2x + 4y = 8 by substitution.
We call them ① and ②.
We want the x and y that make both true.
1 Get x alone in ①
No letter is alone yet.
In ①, x has just 1 in front.
So we get x alone there first.
We want x by itself.
The + 2y is in the way.
To remove + 2y, we take away 2y.
We do it on both sides, so they stay equal.
+ 2y and − 2y make zero.
Cross them out.
Write what is left.
We write the y part first.
Each part keeps its sign.
x is by itself.
We call it ③.
2 Put ③ into ②
In ③, x is now alone.
x is the same as −2y + 4.
So in ②, we write (−2y + 4) in place of x.
The brackets keep it together.
Putting one thing in place of another is called substitution.
3 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!
4 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.
−4y + 4y = 0.
Now we have 8 = 8.
Both letters are gone, and 8 = 8 is always true.
The two equations are the same line.
So every point on the line works.
Let's look back.
First: get x alone in ①.
Then: put ③ into ②.
Last: find y.