System of Equation

Question

the tens digit of a two-digit number is 6 more than the units digit. The number os 2 more than 8 times the sum of the digits. What is the number

Answer 1

T = O + 6 <--- the tens digit is 6 more than the ones digit

T - O = 6

the number is 2 more than 8 times the sum of it's digits....

The number is 10T + O = 8(T+O)+2

10T + O = 8T + 8O + 2

2T - 7O = 2

Putting them together:

2T - 7O = 2

T - O = 6

Solves by elimination: multiplies bottom equation by -2:

2T - 7O = 2

-2T + 2O = -12

-5O = -10 <--- adds them together

O = 2

So then T = O+6 = 2+6 = 8

The number is 82

CHECK:

82 = 80 + 2 = 8*10 + 2 = 8(8+2)+2 <--- 2 more than 8 times the sum of the digits

The number is 82