Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
MediumTwo rails are represented by the equations $x+2y-4=0$ and $2x+4y-12=0$. Represent this situation geometrically.
(N/A) To represent the equations geometrically,we find two solutions for each equation.
For the equation $x+2y-4=0$:
We plot the points $R(0, 2)$ and $S(4, 0)$ to get the line representing $x+2y-4=0$.
For the equation $2x+4y-12=0$:
We plot the points $P(0, 3)$ and $Q(6, 0)$ to get the line representing $2x+4y-12=0$.
Observing the graph,we see that the two lines do not intersect anywhere,which means they are parallel to each other.
For the equation $x+2y-4=0$:
| $x$ | $0$ | $4$ |
| $y = \frac{4-x}{2}$ | $2$ | $0$ |
We plot the points $R(0, 2)$ and $S(4, 0)$ to get the line representing $x+2y-4=0$.
For the equation $2x+4y-12=0$:
| $x$ | $0$ | $6$ |
| $y = \frac{12-2x}{4}$ | $3$ | $0$ |
We plot the points $P(0, 3)$ and $Q(6, 0)$ to get the line representing $2x+4y-12=0$.
Observing the graph,we see that the two lines do not intersect anywhere,which means they are parallel to each other.
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Similar Questions
Form the pair of linear equations for the following problem and find their solution by the substitution method.
$A$ fraction becomes $\frac{9}{11}$ if $2$ is added to both the numerator and the denominator. If $3$ is added to both the numerator and the denominator,it becomes $\frac{5}{6}$. Find the fraction.
$A$ fraction becomes $\frac{9}{11}$ if $2$ is added to both the numerator and the denominator. If $3$ is added to both the numerator and the denominator,it becomes $\frac{5}{6}$. Find the fraction.
Difficult
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 SolutionGraphically,find whether the following pair of equations has no solution,unique solution or infinitely many solutions.
$5x - 8y + 1 = 0$ $...(1)$
$3x - \frac{24}{5}y + \frac{3}{5} = 6$ $...(2)$
$5x - 8y + 1 = 0$ $...(1)$
$3x - \frac{24}{5}y + \frac{3}{5} = 6$ $...(2)$
Medium
View SolutionSolve the following pair of linear equations by the elimination method and the substitution method:
$3x - 5y - 4 = 0$ and $9x = 2y + 7$
$3x - 5y - 4 = 0$ and $9x = 2y + 7$
Difficult
View Solution$k$ ની કઈ કિંમત માટે નીચે આપેલ સુરેખ સમીકરણોની જોડને કોઈ ઉકેલ નથી?
$3x + y = 1$
$(2k - 1)x + (k - 1)y = 2k + 1$
$3x + y = 1$
$(2k - 1)x + (k - 1)y = 2k + 1$
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