Tìm số tự nhiên có hai chữ số.Biết rằng tổng của hai chữ số đó là 10 và nếu đổi cho hai chữ số ấy thì được số mới lớn hơn số cũ là 36

To solve this problem, we can use algebraic equations. Let's denote the tens digit as x and the units digit as y. We are given two pieces of information: 1. The sum of the two digits is 10: $$ 2. If we swap the digits, the new number is greater than the original number by 36: $$ From equation (1), we can express one variable in terms of the other: $$ Substitute this expression for x into equation (2): $$ Simplify and solve for y: $$ $$ $$ $$ $$ Now that we have found the value of y, substitute it back into the expression for x: $$ $$ $$ However, since x and y represent digits, they must be between 0 and 9. Since x cannot be negative, our assumption was incorrect. Let's reconsider our approach to solving this problem. We know that the sum of the two digits is equal to ten. Therefore, if one digit is a certain value, then its complement will be ten minus that value. Let's try different values for one of the digits and see if it leads us to a valid solution. If we let x be equal to one, then its complement would be nine. However, swapping these digits does not result in a number greater than thirty-six. If we let x be equal to two, then its complement would be eight. Swapping these digits results in a number greater than thirty-six: So our final answer is: The two-digit number satisfying the conditions is: $$