The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times the unit digit. Find the number.

Let the digits be (x)(y) where t is the tens digit, and o is the ones digit. We're given:

1. x + y = 10
2. 10x+ y = 15y + 4

Simplifying Equation (2) by subtracting y from each side, we get:
10x = 14y + 4

Rearranging equation (1), we get:
x = 10 - y

Substitute this into simplified equation (2):
10(10 - y) = 14y + 4
100 - 10y = 14y + 4

Typing this equation into our search engine, we get:
y = 4

Plug this into rearranged equation (1), we get:
x = 10 - 4
x = 6

So our number xy is 64.

Let's check our work against equation (1):
6 + 4 ? 10
10 = 10

Let's check our work against equation (2):
10(6)+ 4 ? 15(4) + 4
60 + 4 ? 60 + 4
64 = 64