Step by step
The question
Question: solve 2x + y = −4 and 3x − 2y = 1 by substitution.
We call them ① and ②.
We want the x and y that make both true.
1 Get y alone in ①
No letter is alone yet.
In ①, y has just 1 in front.
So we get y alone there first.
We want y by itself.
The 2x is in the way.
To remove 2x, we take away 2x.
We do it on both sides, so they stay equal.
2x and − 2x make zero.
Cross them out.
Write what is left.
We write the x part first.
Each part keeps its sign.
y is by itself.
We call it ③.
2 Put ③ into ②
In ③, y is now alone.
y is the same as −2x − 4.
So in ②, we write (−2x − 4) in place of y.
The brackets keep it together.
Putting one thing in place of another is called substitution.
3 Find x
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 x terms go together.
3x + 4x = 7x.
Now we have 7x + 8 = 1.
We want x by itself.
The + 8 is in the way.
To remove + 8, we take away 8.
We do it on both sides, so they stay equal.
+ 8 and − 8 make zero.
Cross them out.
1 minus 8 is −7.
Now we have 7x = −7.
7x means 7 times x.
We want just x.
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 x is left.
−7 divided by 7 is −1.
So x = −1.
4 Find y
Now we put x = −1 into ③.
That is 2 − 4.
So y = −2.
So x = −1 and y = −2, both at the same time.
We write it as (−1, −2).
On a graph, it is the point where the two lines meet.
5 Check
Let's check in both equations.
We put x = −1 and y = −2 into ①.
We get −4, the same as the right side.
Now ②.
We get 1, the same as the right side.
Both work.
So the answer is right!
Let's look back.
First: get y alone in ①.
Then: put ③ into ②.
Then: find x.
Then: find y.
Last: check.