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
Given 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 coincident lines.
Easy
View SolutionSolve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{10}{x+y} + \frac{2}{x-y} = 4$
$\frac{15}{x+y} - \frac{5}{x-y} = -2$
$\frac{10}{x+y} + \frac{2}{x-y} = 4$
$\frac{15}{x+y} - \frac{5}{x-y} = -2$
Difficult
View SolutionSolve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{5}{x-1} + \frac{1}{y-2} = 2$
$\frac{6}{x-1} - \frac{3}{y-2} = 1$
$\frac{5}{x-1} + \frac{1}{y-2} = 2$
$\frac{6}{x-1} - \frac{3}{y-2} = 1$
Medium
View SolutionSolve the following pair of linear equations by the substitution method.
$s-t=3$
$\frac{s}{3}+\frac{t}{2}=6$
$s-t=3$
$\frac{s}{3}+\frac{t}{2}=6$
Difficult
View SolutionSolve the following pair of linear equations:
$\frac{x}{a} - \frac{y}{b} = 0$
$ax + by = a^2 + b^2$
$\frac{x}{a} - \frac{y}{b} = 0$
$ax + by = a^2 + b^2$
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