leniar equations in 2 variables

Asked by akshatverma | 9th Aug, 2009, 05:52: PM

Expert Answer:

Let's say the digits are x and y, then the number is 10x + y

"A two digit number is seven times the sum of its digits"

7(x + y) = 10x + y   ...... (1)

3x - 6y = 0 ;

y = x/2  ....(1A)

"..is also equal to twelve less than three times the product of its digits"

3xy -12 = 10x + y  .........(2)

3xy - y = 10x + 12

y = (10x + 12)/(3x - 1)  ..........(3)

Also y = x/2 from (1A)

x/2 = (10x +12)/(3x - 1)

Solving for x, we get the quadratic equation,

x2 - 7x - 8 = 0 ;   (x - 8)(x + 1) = 0 ; so x = 8 or x = -1;

Hence y = x/2 = 4 since it's a digit and cann't be fraction.

Therefore the number is, 84.

Regards,

Team,

TopperLearning.

Answered by  | 9th Aug, 2009, 07:45: PM

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