Mathematics
Form the pair of linear equations in the following problem, and find their solutions (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.
Linear Equations
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Answer
Let x be the digit at ten's place and y be the digit at units place.
Number = 10x + y
Given,
Sum of two digits is 9.
∴ x + y = 9 …….(1)
Given,
Nine times this number is twice the number obtained by reversing the order of the digits.
∴ 9(10x + y) = 2(10y + x)
⇒ 90x + 9y = 20y + 2x
⇒ 90x - 2x + 9y - 20y = 0
⇒ 88x - 11y = 0
⇒ 11(8x - y) = 0
⇒ 8x - y = 0 ……..(2)
Adding equations (1) and (2), we get :
⇒ x + y + (8x - y) = 9
⇒ x + 8x + y - y = 9
⇒ 9x = 9
⇒ x =
⇒ x = 1.
Substituting value of x in equation (2), we get :
⇒ 8(1) - y = 0
⇒ 8 - y = 0
⇒ y = 8.
Number = (10x + y) = 10 × 1 + 8 = 10 + 8 = 18.
Hence, pair of linear equations are x + y = 9, 8x - y = 0, where x and y are respectively the tens and units digits of the number and number = 18.
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