Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
MediumSolve the following pair of equations by substitution method:
$7x - 15y = 2$ $...(1)$
$x + 2y = 3$ $...(2)$
$7x - 15y = 2$ $...(1)$
$x + 2y = 3$ $...(2)$
(N/A) Step $1:$ We pick either of the equations and write one variable in terms of the other. Let us consider Equation $(2)$.
$x + 2y = 3$
We can write it as $x = 3 - 2y$ $...(3)$
Step $2:$ Substitute the value of $x$ from Equation $(3)$ into Equation $(1)$. We get:
$7(3 - 2y) - 15y = 2$
$21 - 14y - 15y = 2$
$-29y = 2 - 21$
$-29y = -19$
Therefore,$y = \frac{19}{29}$
Step $3:$ Substituting this value of $y$ in Equation $(3)$,we get:
$x = 3 - 2\left(\frac{19}{29}\right)$
$x = 3 - \frac{38}{29}$
$x = \frac{87 - 38}{29} = \frac{49}{29}$
Therefore,the solution is $x = \frac{49}{29}, y = \frac{19}{29}$.
$x + 2y = 3$
We can write it as $x = 3 - 2y$ $...(3)$
Step $2:$ Substitute the value of $x$ from Equation $(3)$ into Equation $(1)$. We get:
$7(3 - 2y) - 15y = 2$
$21 - 14y - 15y = 2$
$-29y = 2 - 21$
$-29y = -19$
Therefore,$y = \frac{19}{29}$
Step $3:$ Substituting this value of $y$ in Equation $(3)$,we get:
$x = 3 - 2\left(\frac{19}{29}\right)$
$x = 3 - \frac{38}{29}$
$x = \frac{87 - 38}{29} = \frac{49}{29}$
Therefore,the solution is $x = \frac{49}{29}, y = \frac{19}{29}$.
Explore More
Similar Questions
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method.
The area of a rectangle gets reduced by $9$ square units,if its length is reduced by $5$ units and breadth is increased by $3$ units. If we increase the length by $3$ units and the breadth by $2$ units,the area increases by $67$ square units. Find the dimensions of the rectangle.
The area of a rectangle gets reduced by $9$ square units,if its length is reduced by $5$ units and breadth is increased by $3$ units. If we increase the length by $3$ units and the breadth by $2$ units,the area increases by $67$ square units. Find the dimensions of the rectangle.
Medium
View SolutionTwo rails are represented by the equations $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$. Will the rails cross each other?
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.
$3x - 5y = 20$
$6x - 10y = 40$
$3x - 5y = 20$
$6x - 10y = 40$
Medium
View SolutionFormulate the following problems as a pair of equations, and hence find their solutions:
Ritu can row downstream $20\, km$ in $2\, hours,$ and upstream $4\, km$ in $2\, hours.$ Find her speed of rowing in still water and the speed of the current.
Ritu can row downstream $20\, km$ in $2\, hours,$ and upstream $4\, km$ in $2\, hours.$ Find her speed of rowing in still water and the speed of the current.
Easy
View SolutionSolve the following pair of equations by reducing them to a pair of linear equations:
$\frac{4}{x} + 3y = 14$
$\frac{3}{x} - 4y = 23$
$\frac{4}{x} + 3y = 14$
$\frac{3}{x} - 4y = 23$
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