A two- digit number is formed by either subtracting 17 from nine times the sum of the digits or by - Maths - Pair of Linear Equations in Two Variables

Question

A two- digit number is formed by either subtracting 17 from nine
times the sum of the digits or by adding 21 to 13 times the
difference of the digits Find the number

Varun.Rawat · Accepted Answer

Let the digit at units place = xLet the digit at tens place = yNow, original number = 10y+xNow, according to first condition :    9x+y - 17 = 10y+x⇒8x - y = 17      
1According to second condition :13x-y + 21 = 10y+x    or   13y-x + 21 = 10y+x12x - 23y = -21    
2  or   3y-14x = -21    
3SOLVING 1 AND 2 :Multiply 1 by 3 and 2 by 2, we get24x - 3y = 51   
424x - 46y = -42    
5Subtracting 5 from 4, we get43y = 93 ⇒y = 9343    not possible as the digit can not be in fractionSOLVING 1 AND 3 :Multiply 1 by 3 , we get24x - 3y = 51     
6Adding 3 and 6, we get10x = 30  ⇒x = 3Now, from 1, we get8×3 - y = 17⇒y = 7So, original number = 10×7+3 = 73

A two- digit number is formed by either subtracting 17 from nine times the sum of the digits or by adding 21 to 13 times the difference of the digits. Find the number