Question

What is the two-digit number?

I.

The difference between the two digits is 9.

II.

The sum of the digits is equal to the difference between the two digits.

Answer 1

9 and 0

Explanation:

Let's assume, the first digit is x and the second one is y:

Let's write 2 equations according to the given information and put them into a system:

{x - y = 9,

{x + y = 9;

Let's make x the subject from the 1st equation:

x = 9 + y

Replace x in the 2nd equation with its new value from the 1st equation:

(9 + y) + y = 9

Eliminate the brackets:

9 + y + y = 9

Collect like-terms:

2y = 9 - 9

2y = 0 / : 2

y = 0

x = 9 + 0 = 9