Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
EasyForm the pair of linear equations for the following problem and find their solution by the substitution method.
The difference between two numbers is $26$ and one number is three times the other. Find the numbers.
The difference between two numbers is $26$ and one number is three times the other. Find the numbers.
(N/A) Let the first number be $x$ and the other number be $y$ such that $y > x$.
According to the given information:
$y = 3x$ $...(1)$
$y - x = 26$ $...(2)$
On substituting the value of $y$ from equation $(1)$ into equation $(2)$,we obtain:
$3x - x = 26$
$2x = 26$
$x = 13$ $...(3)$
Substituting the value of $x$ in equation $(1)$,we obtain:
$y = 3(13) = 39$
Hence,the two numbers are $13$ and $39$.
According to the given information:
$y = 3x$ $...(1)$
$y - x = 26$ $...(2)$
On substituting the value of $y$ from equation $(1)$ into equation $(2)$,we obtain:
$3x - x = 26$
$2x = 26$
$x = 13$ $...(3)$
Substituting the value of $x$ in equation $(1)$,we obtain:
$y = 3(13) = 39$
Hence,the two numbers are $13$ and $39$.
Explore More
Similar Questions
Solve the following pair of linear equations by the substitution method.
$3x - y = 3$
$9x - 3y = 9$
$3x - y = 3$
$9x - 3y = 9$
Medium
View SolutionOn comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}},$ find out whether the lines representing the following pairs of linear equations intersect at a point,are parallel,or are coincident:
$9x + 3y + 12 = 0$
$18x + 6y + 24 = 0$
$9x + 3y + 12 = 0$
$18x + 6y + 24 = 0$
Easy
View SolutionWhich 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 SolutionWhich of the following pairs of linear equations has a unique solution,no solution,or infinitely many solutions? In case there is a unique solution,find it by using the cross-multiplication method.
$x - 3y - 3 = 0$
$3x - 9y - 2 = 0$
$x - 3y - 3 = 0$
$3x - 9y - 2 = 0$
Easy
View SolutionFor what value of $k$ will the following pair of linear equations have infinitely many solutions?
$kx + 3y - (k - 3) = 0$
$12x + ky - k = 0$
$kx + 3y - (k - 3) = 0$
$12x + ky - k = 0$
Difficult
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