Question

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number
obtained by reversing the order of the digits."
Represent the above statements by two linear equations in two variables
​

Answer 1

Step-by-step explanation:

Let the two digit number be 'XY'

Its common form:

10 X + Y

Sum of digits = X + Y

X + Y = 9

9*XY = 2*XY

9* (10 X + Y) = 2* (10 Y + X)

90 X + 9 Y = 20 Y + 2 X

88 X = 11 Y

8 X = Y

8 X - Y = 0

The linear equations are:

X + Y = 9

8 X - Y = 0

Additional info:

8 X = Y

X + 8 X = 9

9 X  = 9

X = 1

Y = 8

Hence number = 18