Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
EasyGiven the linear equation $2x + 3y - 8 = 0$,write another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines.
(N/A) For a pair of linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to represent intersecting lines,the condition is $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$.
Given the equation $2x + 3y - 8 = 0$,we have $a_1 = 2$ and $b_1 = 3$.
We need to choose $a_2$ and $b_2$ such that $\frac{2}{a_2} \neq \frac{3}{b_2}$.
If we choose $a_2 = 3$ and $b_2 = 2$,then $\frac{2}{3} \neq \frac{3}{2}$,which satisfies the condition.
Thus,one such equation is $3x + 2y - 5 = 0$ (or any other equation satisfying the condition).
Given the equation $2x + 3y - 8 = 0$,we have $a_1 = 2$ and $b_1 = 3$.
We need to choose $a_2$ and $b_2$ such that $\frac{2}{a_2} \neq \frac{3}{b_2}$.
If we choose $a_2 = 3$ and $b_2 = 2$,then $\frac{2}{3} \neq \frac{3}{2}$,which satisfies the condition.
Thus,one such equation is $3x + 2y - 5 = 0$ (or any other equation satisfying the condition).
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Similar Questions
Solve the following pair of linear equations by the substitution method:
$\frac{3x}{2} - \frac{5y}{3} = -2$
$\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$
$\frac{3x}{2} - \frac{5y}{3} = -2$
$\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$
Medium
View SolutionForm the pair of linear equations for the following problem and find their solution by the substitution method.
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of $10 \, km$,the charge paid is ₹ $105$ and for a journey of $15 \, km$,the charge paid is ₹ $155$. What are the fixed charges and the charge per $km$? How much does a person have to pay for travelling a distance of $25 \, km$?
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of $10 \, km$,the charge paid is ₹ $105$ and for a journey of $15 \, km$,the charge paid is ₹ $155$. What are the fixed charges and the charge per $km$? How much does a person have to pay for travelling a distance of $25 \, km$?
Difficult
View SolutionSolve the following pair of equations by reducing them to a pair of linear equations:
$\frac{1}{2x} + \frac{1}{3y} = 2$
$\frac{1}{3x} + \frac{1}{2y} = \frac{13}{6}$
$\frac{1}{2x} + \frac{1}{3y} = 2$
$\frac{1}{3x} + \frac{1}{2y} = \frac{13}{6}$
Medium
View SolutionSolve the following pair of linear equations by the substitution method.
$0.2 x + 0.3 y = 1.3$
$0.4 x + 0.5 y = 2.3$
$0.2 x + 0.3 y = 1.3$
$0.4 x + 0.5 y = 2.3$
Difficult
View SolutionSolve the following pair of equations by reducing them to a pair of linear equations:
$\frac{5}{x-1} + \frac{1}{y-2} = 2$
$\frac{6}{x-1} - \frac{3}{y-2} = 1$
$\frac{5}{x-1} + \frac{1}{y-2} = 2$
$\frac{6}{x-1} - \frac{3}{y-2} = 1$
Difficult
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