(D) Given equations are:$(1)$ $\frac{2}{x} + \frac{3}{y} = 17$$(2)$ $\frac{3}{x} + \frac{2}{y} = 13$Adding equation $(1)$ and equation $(2)$:$(\frac{2

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(D) Given equations are:$(1)$ $\frac{2}{x} + \frac{3}{y} = 17$$(2)$ $\frac{3}{x} + \frac{2}{y} = 13$Adding equation $(1)$ and equation $(2)$:$(\frac{2}{x} + \frac{3}{x}) + (\frac{3}{y} + \frac{2}{y}) = 17 + 13$$\frac{5}{x} + \frac{5}{y} = 30$Taking $5$ as a common factor:$5(\frac{1}{x} + \frac{1}{y}) = 30$Dividing both sides by $5$:$\frac{1}{x} + \frac{1}{y} = \frac{30}{5} = 6$Thus,the value is $6$.

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

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For a pair of equations $\frac{2}{x} + \frac{3}{y} = 17$ and $\frac{3}{x} + \frac{2}{y} = 13$,find the value of $\frac{1}{x} + \frac{1}{y}$.

A
$5$
B
$30$
C
$20$
D
$6$

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

Find the solution of the pair of equations $\frac{x}{10} + \frac{y}{5} - 1 = 0$ and $\frac{x}{8} + \frac{y}{6} = 15$. Hence,find $\lambda$ if $y = \lambda x + 5$.

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The graph of the equation $\ldots \ldots \ldots \ldots$ is a line perpendicular to the $Y-axis.$

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Half the perimeter of a rectangular garden,whose length is $4 \, m$ more than its width,is $36 \, m$. Represent this as a pair of linear equations in two variables.

Medium

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By the graphical method,find whether the following pair of equations are consistent or not. If consistent,solve them.
$x - 2y = 6$
$3x - 6y = 0$

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From the pair of equations $x + 2y = 8 \dots(1)$ and $3x - 4y = -6 \dots(2)$,the first equation should be multiplied by ............. to eliminate $y$.

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For a pair of equations $\frac{2}{x} + \frac{3}{y} = 17$ and $\frac{3}{x} + \frac{2}{y} = 13$,find the value of $\frac{1}{x} + \frac{1}{y}$.

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Find the solution of the pair of equations $\frac{x}{10} + \frac{y}{5} - 1 = 0$ and $\frac{x}{8} + \frac{y}{6} = 15$. Hence,find $\lambda$ if $y = \lambda x + 5$.

The graph of the equation $\ldots \ldots \ldots \ldots$ is a line perpendicular to the $Y-axis.$

Half the perimeter of a rectangular garden,whose length is $4 \, m$ more than its width,is $36 \, m$. Represent this as a pair of linear equations in two variables.

By the graphical method,find whether the following pair of equations are consistent or not. If consistent,solve them.$x - 2y = 6$$3x - 6y = 0$

From the pair of equations $x + 2y = 8 \dots(1)$ and $3x - 4y = -6 \dots(2)$,the first equation should be multiplied by ............. to eliminate $y$.

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By the graphical method,find whether the following pair of equations are consistent or not. If consistent,solve them.
$x - 2y = 6$
$3x - 6y = 0$