Question

sum of the digit of a two digit number is 14 if we add 18 to the original number the digit interchange their places write two equations for these two statements​

Answer 1

case 1 sum of the digits.

X+Y=14

case 2 digits interchange

10x+y+18=10y+x. (xy be number can be written as x tens + y ones so 10x+y)

9x-9y=-18

x-y=-2

the two equations are

x+y=14

x-y=-2

solving x is 6 and y is 8

the original number is 68

Answer 2

let the number at ten's place be x and number at unit's place be y.

by the first condition,

x+y=14 ..........1

by the second condition,

10x+y+18=10y+x

10x-x-10y+y=-18

9x-9y=-18

dividing by two on both the sides

x-y=-2...........2

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