Step by step
The question
Question: solve 3x + 2y = 16 and x − 2y = 0.
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: 2y and −2y.
They are opposites.
Added, they make zero.
2y and −2y make zero.
Cross them out.
We add ① and ②: the x parts together, and the numbers together.
3x + x = 4x.
16 + 0 = 16.
Now we have 4x = 16.
Is x alone now?
Not yet: 4x means 4 times x.
How do we remove it?
2 Find x
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
They cancel each other.
So just x is left.
16 divided by 4 is 4.
So x = 4.
So after step 2: we divided by 4, and now we have x = 4.
3 Find y
We put x = 4 into ①.
3 times 4 is 12.
Now we have 12 + 2y = 16.
We want y by itself.
The 12 is in the way.
Is y alone now?
Not yet: + 12 is still with y.
To remove 12, we take away 12.
We do it on both sides, so they stay equal.
12 and − 12 cancel each other.
They make zero.
16 minus 12 is 4.
Now we have 2y = 4.
2y means 2 times y.
Is y alone now?
Not yet: 2y means 2 times y.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
They cancel each other.
So just y is left.
4 divided by 2 is 2.
So y = 2.
So x = 4 and y = 2, both at the same time.
We write it as (4, 2).
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 = 2 into ①.
We get 16, the same as the right side.
Now ②.
We get 0, the same as the right side.
Both work.
So the answer is right!
5 Pick the choice
Our answer is (x, y) = (4, 2).
That is choice C.
6 Why not the others
A is (2, 4).
Wrong: x and y swapped.
B is (4, −2).
Wrong: 4 − 2y = 0 gives y = 2, not −2.
D is (16, 8).
Wrong: 4x = 16 means x = 4: forgot to divide by 4.
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.