Form the pair of linear equations in the foll | vedclass

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(A) Let the unit digit be $x$ and the tens digit be $y$. Then,the number is $10y + x$.According to the first condition,the sum of the digits is $9$:$x

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(A) Let the unit digit be $x$ and the tens digit be $y$. Then,the number is $10y + x$.According to the first condition,the sum of the digits is $9$:$x + y = 9$ $...(1)$According to the second condition,nine times the number is twice the number obtained by reversing the digits:$9(10y + x) = 2(10x + y)$$90y + 9x = 20x + 2y$$88y - 11x = 0$Dividing by $11$,we get:$8y - x = 0$ or $-x + 8y = 0$ $...(2)$Adding equation $(1)$ and $(2)$:$(x + y) + (-x + 8y) = 9 + 0$$9y = 9$$y = 1$Substituting $y = 1$ in equation $(1)$:$x + 1 = 9$$x = 8$Therefore,the number is $10y + x = 10(1) + 8 = 18$.

Form the pair of linear equations in the following problems,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.

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Form the pair of linear equations in the following problems,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.