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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.
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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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