Question

A number of two digit such that 4 times the unit digit is 5> thrice the 10 digit, when the digit are reverse the number is increase by 9. find the number

Answer 1

Let xy be the number x in ten's place and y in units place

4y=3x+5

4y-3x=5................(1)

10y+x= 10x+y+9

9y-9x=9

/9

y-x=1...................(2)

-3 x + 4 y = 5 .............1

-1 x + 1 y = 1 .............2

Eliminate y

multiply (1)by -1

Multiply (2) by 4

3 x -4 y = -5

-4 x + 4 y = 4

Add the two equations

-1 x = -1

/ -1

x = 1

plug value of x in (1)

-3 x + 4 y = 5

-3 + 4 y = 5

4 y = 5 + 3

4 y = 8

y = 2

The number is 12