(B) Given equations are:$1) \, 2x + 3y = 7$$2) \, 6x + 9y = 23$Check the ratio of coefficients:$\frac{a_1}{a_2} = \frac{2}{6} = \frac{1}{3}$$\frac{b_1

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$\text{No solution } (\varnothing)$

(B) Given equations are:$1) \, 2x + 3y = 7$$2) \, 6x + 9y = 23$Check the ratio of coefficients:$\frac{a_1}{a_2} = \frac{2}{6} = \frac{1}{3}$$\frac{b_1}{b_2} = \frac{3}{9} = \frac{1}{3}$$\frac{c_1}{c_2} = \frac{7}{23}$Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$,the lines are parallel to each other.Therefore,the system of equations has no solution,denoted by $\varnothing$.

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

Medium

Solve the following pair of linear equations by the method of substitution: $2x + 3y = 7$ and $6x + 9y = 23$.

A
$(2, 2)$
B
$\text{No solution } (\varnothing)$
C
$(1, 1.5)$
D
$(0, -3)$

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Mix Examples - Pair of Linear Equations in Two Variables

Solve the following pair of linear equations: $\frac{5}{x-1} + \frac{1}{y-2} = 2$ and $\frac{6}{x-1} - \frac{3}{y-2} = 1$.

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The solution of the pair of equations $x+2=0$ and $y-1=0$ is $(x, y) = \dots$

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Solve the following pairs of equations:
$\frac{2xy}{x+y} = \frac{3}{2}$
$\frac{xy}{2x-y} = \frac{-3}{10}, \quad x+y \neq 0, 2x-y \neq 0$

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If $\frac{5}{x}-\frac{4}{y}=4$ and $\frac{4}{x}-\frac{5}{y}=5,$ then $\frac{1}{x}-\frac{1}{y}=\ldots \ldots \ldots \ldots .(x, y \neq 0)$

Medium

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Solve the following pair of linear equations: $\frac{9}{a} + \frac{8}{b} = 7$ and $\frac{2}{a} - \frac{3}{b} = -8$.

Medium

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Solve the following pair of linear equations by the method of substitution: $2x + 3y = 7$ and $6x + 9y = 23$.

Similar Questions

Solve the following pair of linear equations: $\frac{5}{x-1} + \frac{1}{y-2} = 2$ and $\frac{6}{x-1} - \frac{3}{y-2} = 1$.

The solution of the pair of equations $x+2=0$ and $y-1=0$ is $(x, y) = \dots$

Solve the following pairs of equations:$\frac{2xy}{x+y} = \frac{3}{2}$$\frac{xy}{2x-y} = \frac{-3}{10}, \quad x+y \neq 0, 2x-y \neq 0$

If $\frac{5}{x}-\frac{4}{y}=4$ and $\frac{4}{x}-\frac{5}{y}=5,$ then $\frac{1}{x}-\frac{1}{y}=\ldots \ldots \ldots \ldots .(x, y \neq 0)$

Solve the following pair of linear equations: $\frac{9}{a} + \frac{8}{b} = 7$ and $\frac{2}{a} - \frac{3}{b} = -8$.

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Solve the following pairs of equations:
$\frac{2xy}{x+y} = \frac{3}{2}$
$\frac{xy}{2x-y} = \frac{-3}{10}, \quad x+y \neq 0, 2x-y \neq 0$