Question

What is the two-digit number?

I.

Sum of the digits is 7.

II.

Difference between the number and the number obtained by interchanging the digits is 9.

III.

Digit in the ten's place is bigger than the digit in the unit's place by 1.

Answer 1

3 and 4

Explanation:

Let's assume, the first digit (ten's place) is x and the second one (unit's place) is y

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

{x + y = 7,

{x - y = 1;

Let's make x the subject from the 1st equation (it doesn't matter which equation or term (x or y) you choose):

x = 7 - y

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

(7 - y) - y = 1

Eliminate the brackets:

7 - y - y = 1

Collect like-terms (don't forget, when moving terms to the other side, make sure to change their sign into the opposite of the previous one):

-2y = 1 - 7

-2y = -6 / : (-2)

y = 3

x = 7 - 3 = 4