I am a two-digit number. The sum of my two digit is 9. The difference of my digits is 5. What number am I?

72

Step-by-step explanation:

The two digit number can be represented by xy, where x and y must add to 9 and x - y must subtract to 5. Make a system of equations.

x + y = 9 x - y = 5

Use the elimination method and add the terms from top to bottom like so. The y and - y cancel out.

2x = 14

Divide both sides by 2.

x = 7

Substitute 7 for x into the first equation (either eqn would work).

(7) + y = 9

Subtract 7 from both sides.

y = 2

Combine these two together; xy - -> (7) (2) - -> 72.

The number is 72.