Step by step
The question
Question: if 2x − 3y = 5, what is 6x − 9y?
We want 6x − 9y.
Let's look for it inside the equation.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Compare the two
Look at 6x − 9y and 2x − 3y.
We compare them part by part.
6 divided by 2 is 3.
So 6x is 3 times 2x.
9 divided by 3 is 3.
So 9y is 3 times 3y.
Every part of 6x − 9y is 3 times a part of 2x − 3y.
2 Multiply by 3
So we multiply both sides by 3.
We do it on both sides, so they stay equal.
Times 3 goes to every part.
3 times 5 is 15.
Careful!
Both sides are times 3.
5 becomes 15.
3 times 2x is 6x.
3 times −3y is −9y.
So 6x − 9y = 15!
3 Check
We can't find x and y on their own: many pairs work.
Let's check with one pair.
We pick x = 4, so that y is a small whole number.
With y = 1, 2x − 3y is 2 × 4 − 3 × 1 = 8 − 3 = 5.
It fits the question.
And 6x − 9y is 6 × 4 − 9 × 1 = 24 − 9 = 15.
The same answer.
It works!
4 Pick the choice
Our answer is 6x − 9y = 15.
That is choice C.
5 Why not the others
A is 5.
Wrong: that is 2x − 3y, not 6x − 9y.
That is the Careful mistake from before.
B is 10.
Wrong: doubled: 6x − 9y is 3 times 2x − 3y.
D is 45.
Wrong: 5 × 9: used the 9, not 3.
Let's look back.
First: compare the two.
Then: multiply by 3.
Then: check.
Then: pick the choice.
Last: why not the others.