Answer: the original number is 62
Step-by-step explanation: Let’s solve this problem using Cramer’s Rule. Let the ten’s digit be x and the unit’s digit be y. Then the original number is 10x + y. If we interchange the digits, the new number becomes 10y + x. According to the problem, the sum of the digits is 8, so we can write the first equation as x + y = 8. The new number is 36 less than the original number, so we can write the second equation as 10y + x = 10x + y - 36. Simplifying this equation gives us 9y - 9x = -36 or y - x = -4.
Now we have a system of two linear equations: x + y = 8 y - x = -4
We can solve this system using Cramer’s Rule. The determinant of the coefficient matrix is |1 1| |-1 1| = 1 * 1 - (-1) * 1 = 2.
The determinant of the matrix obtained by replacing the first column of the coefficient matrix with the constants is |8 1| |-4 1| = 8 * 1 - (-4) * 1 = 12.
The determinant of the matrix obtained by replacing the second column of the coefficient matrix with the constants is |1 8| |-1 -4| = 1 * (-4) - (-1) * 8 = -4.
According to Cramer’s Rule, x = Dx/D = 12/2 = 6 and y = Dy/D = (-4)/2 = -2.
So, the original number is 62.