(B) Let the tens digit be $x$ and the units digit be $y$.The number is $10x + y$.According to the problem:$x + y = 9$ (Equation $1$)$x - y = 1$ (Equat

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(B) Let the tens digit be $x$ and the units digit be $y$.The number is $10x + y$.According to the problem:$x + y = 9$ (Equation $1$)$x - y = 1$ (Equation $2$)Adding Equation $1$ and Equation $2$:$(x + y) + (x - y) = 9 + 1$$2x = 10$$x = 5$Substituting $x = 5$ in Equation $1$:$5 + y = 9$$y = 4$Therefore,the number is $10(5) + 4 = 54$.

Class 10 Mathematics Pair of Linear Equations in Two Variables Mix Examples - Pair of Linear Equations in Two Variables

Easy

The sum of the digits of a two-digit number is $9$ and the difference is $1$. The number is ............

A
$27$
B
$54$
C
$87$
D
$63$

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

For the pair of equations $2x + 3y = 10$ and $3x - y = 4$,find the value of $x$.

Medium

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Four years ago,the sum of the ages of four persons was $40$ years. After two years,the sum of the ages of the same four persons will be ............ years.

Medium

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For all real values of $c,$ the pair of equations $x-2y=8$ and $5x-10y=c$ have a unique solution. Justify whether it is true or false.

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Draw the graphs of the lines $x=-2$ and $y=3$. Write the vertices of the figure formed by these lines,the $x$-axis and the $y$-axis. Also,find the area of the figure.

Medium

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Do the following pair of linear equations have no solution? Justify your answer.
$y + 6x = 6$ and $y = 2x$

Medium

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The sum of the digits of a two-digit number is $9$ and the difference is $1$. The number is ............

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For the pair of equations $2x + 3y = 10$ and $3x - y = 4$,find the value of $x$.

Four years ago,the sum of the ages of four persons was $40$ years. After two years,the sum of the ages of the same four persons will be ............ years.

For all real values of $c,$ the pair of equations $x-2y=8$ and $5x-10y=c$ have a unique solution. Justify whether it is true or false.

Draw the graphs of the lines $x=-2$ and $y=3$. Write the vertices of the figure formed by these lines,the $x$-axis and the $y$-axis. Also,find the area of the figure.

Do the following pair of linear equations have no solution? Justify your answer.$y + 6x = 6$ and $y = 2x$

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Do the following pair of linear equations have no solution? Justify your answer.
$y + 6x = 6$ and $y = 2x$