Step by step
The question
Question: if x − 2y = 3, what is 5x − 10y?
We want 5x − 10y.
Let's look for it inside the equation.
1 Compare the two
Look at 5x − 10y and x − 2y.
We compare them part by part.
5x is 5 times x.
10 divided by 2 is 5.
So 10y is 5 times 2y.
Every part of 5x − 10y is 5 times a part of x − 2y.
2 Multiply by 5
So we multiply both sides by 5.
We do it on both sides, so they stay equal.
Times 5 goes to every part.
5 times 3 is 15.
Careful!
Both sides are times 5.
3 becomes 15.
5 times x is 5x.
5 times −2y is −10y.
So 5x − 10y = 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 = 5, so that y is a small whole number.
With y = 1, x − 2y is 5 − 2 × 1 = 5 − 2 = 3.
It fits the question.
And 5x − 10y is 5 × 5 − 10 × 1 = 25 − 10 = 15.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: multiply by 5.
Last: check.