leniar equations in 2 variables
Asked by akshatverma | 9th Aug, 2009, 05:52: PM
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.
Answered by | 9th Aug, 2009, 07:45: PM
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