Step by step
The question
Question: solve 2x + y = 11 and x − y = 1.
There are four choices.
First we solve it, the normal way.
Then we pick.
We call them ① and ②.
We want the x and y that make both true.
No letter is alone here.
So we add the equations to remove one letter.
This way is called elimination.
1 Add the equations
Look at y: y and −y.
They are opposites.
Added, they make zero.
y and −y make zero.
Cross them out.
We add ① and ②: the x parts together, and the numbers together.
2x + x = 3x.
11 + 1 = 12.
Now we have 3x = 12.
Is x alone now?
Not yet: 3x means 3 times x.
How do we remove it?
2 Find 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.
They cancel each other.
So just x is left.
12 divided by 3 is 4.
So x = 4.
So after step 2: we divided by 3, and now we have x = 4.
3 Find y
We put x = 4 into ①.
2 times 4 is 8.
Now we have 8 + y = 11.
We want y by itself.
The 8 is in the way.
Is y alone now?
Not yet: + 8 is still with y.
To remove 8, we take away 8.
We do it on both sides, so they stay equal.
8 and − 8 cancel each other.
They make zero.
11 minus 8 is 3.
So y = 3.
So x = 4 and y = 3, both at the same time.
We write it as (4, 3).
On a graph, it is the point where the two lines meet.
4 Check
Let's check in both equations.
We put x = 4 and y = 3 into ①.
We get 11, the same as the right side.
Now ②.
We get 1, the same as the right side.
Both work.
So the answer is right!
5 Pick the choice
Our answer is (x, y) = (4, 3).
That is choice B.
6 Why not the others
A is (3, 4).
Wrong: x and y swapped.
C is (4, 5).
Wrong: x − y = 1 means y = x − 1, not x + 1.
D is (12, 11).
Wrong: 3x = 12, but we still had to divide by 3.
Let's look back.
First: add the equations.
Then: find x.
Then: find y.
Then: check.
Then: pick the choice.
Last: why not the others.