Answer: 28
Step-by-step explanation:
Let x represent the digit in the tens place and y represent the digit in the ones place. xy → 10x + y
The square of the sum of the digits is 100.
EQ1: (x + y)² = 100 → x + y = 10
2 is subtracted from 3 times the number is the digits reversed.
EQ2: 3(10x + y) - 2 = 10y + x → 30x + 3y - 2 = 10y + x → 29x - 7y = 2
Solve the system of equations using the Elimination method:
EQ1: x + y = 10 → 7(x + y = 10) → 7x + 7y = 70
EQ2: 29x - 7y = 2 → 1(29x - 7y = 2 → 29x - 7y = 2
36x = 72
÷36 ÷36
x = 2
Substitute x = 2 into either of the equations to solve for y.:
EQ1: x + y = 10
2 + y = 10
y = 8
The digit is: 28
