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

$18$

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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 $9$:$x + y = 9$ $...(1)$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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Solve the following pair of linear equations by the elimination method and the substitution method:
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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.

Similar Questions

Solve the following pair of linear equations by the elimination method and the substitution method:$3x - 5y - 4 = 0$ and $9x = 2y + 7$

Solve the following pair of equations by reducing them to a pair of linear equations:$\frac{1}{3x+y} + \frac{1}{3x-y} = \frac{3}{4}$$\frac{1}{2(3x+y)} - \frac{1}{2(3x-y)} = -\frac{1}{8}$

Solve the following pair of linear equations by the elimination method and the substitution method:$x+y=5$ and $2x-3y=4$

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent.$2x - 3y = 8$; $4x - 6y = 9$

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}},$ find out whether the following pair of linear equations are consistent or inconsistent.$3x + 2y = 5; \quad 2x - 3y = 7$