Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
MediumSolve the following pair of linear equations by the substitution method.
$3x - y = 3$
$9x - 3y = 9$
$3x - y = 3$
$9x - 3y = 9$
(D) Given equations are:
$3x - y = 3$ $...(1)$
$9x - 3y = 9$ $...(2)$
From equation $(1)$,we can express $y$ in terms of $x$:
$y = 3x - 3$ $...(3)$
Substituting the value of $y$ from equation $(3)$ into equation $(2)$:
$9x - 3(3x - 3) = 9$
$9x - 9x + 9 = 9$
$9 = 9$
Since $9 = 9$ is a true statement for all values of $x$,the two equations are coincident lines.
Therefore,the given pair of linear equations has infinitely many solutions.
The relationship between the variables is given by $y = 3x - 3$.
$3x - y = 3$ $...(1)$
$9x - 3y = 9$ $...(2)$
From equation $(1)$,we can express $y$ in terms of $x$:
$y = 3x - 3$ $...(3)$
Substituting the value of $y$ from equation $(3)$ into equation $(2)$:
$9x - 3(3x - 3) = 9$
$9x - 9x + 9 = 9$
$9 = 9$
Since $9 = 9$ is a true statement for all values of $x$,the two equations are coincident lines.
Therefore,the given pair of linear equations has infinitely many solutions.
The relationship between the variables is given by $y = 3x - 3$.
Explore More
Similar Questions
Which of the following pairs of linear equations are consistent/inconsistent? If consistent,obtain the solution graphically:
$x+y=5, \quad 2x+2y=10$
$x+y=5, \quad 2x+2y=10$
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
View SolutionForm 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 SolutionPlaces $A$ and $B$ are $100 \ km$ apart on a highway. One car starts from $A$ and another from $B$ at the same time. If the cars travel in the same direction at different speeds,they meet in $5 \ hours$. If they travel towards each other,they meet in $1 \ hour$. What are the speeds of the two cars?
Easy
View SolutionForm the pair of linear equations for the following problem and find their solution by the substitution method.
The larger of two supplementary angles exceeds the smaller by $18^{\circ}$. Find the angles.
The larger of two supplementary angles exceeds the smaller by $18^{\circ}$. Find the angles.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo