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Questions
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
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. Find the number.
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. Find the number.
Solution
Let the units digit of the number be x.
And the tens digit is y.
So the real number will be = 10y + x,
And reversed number = 10x + y
Situation I
x + y = 9 ...(i)
Situation II
9(number) = 2(flipped number)
or 9(10y + x) = 2(10x + y)
or 90y + 9x = 20x + 2y
or 20x – 9x + 2y – 90y = 0
or 11x – 88y = 0
or x – 8y = 0
or x = 8y ...(ii)
By substituting x = 8y in equation (i)
x + y = 9
or 8y + y = 9
or 9y = 9
or y = 1
Substituting y = 1 into equation two
x = 8y = 8 × 1 = 8
Hence, required number = 10y + x
= 10 × 1 + 8
= 18
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