Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
MediumSolve the following pair of linear equations by the elimination method and the substitution method:
$3x + 4y = 10$ and $2x - 2y = 2$
$3x + 4y = 10$ and $2x - 2y = 2$
(N/A) By elimination method:
$3x + 4y = 10$ $...(1)$
$2x - 2y = 2$ $...(2)$
Multiplying equation $(2)$ by $2$,we obtain:
$4x - 4y = 4$ $...(3)$
Adding equation $(1)$ and $(3)$,we obtain:
$7x = 14$
$x = 2$ $...(4)$
Substituting $x = 2$ in equation $(1)$,we obtain:
$3(2) + 4y = 10$
$6 + 4y = 10$
$4y = 4$
$y = 1$
Hence,$x = 2, y = 1$.
By substitution method:
From equation $(2)$,we obtain:
$2x = 2 + 2y$
$x = 1 + y$ $...(5)$
Putting this value in equation $(1)$,we obtain:
$3(1 + y) + 4y = 10$
$3 + 3y + 4y = 10$
$7y = 7$
$y = 1$
Substituting the value $y = 1$ in equation $(5)$,we obtain:
$x = 1 + 1 = 2$
Therefore,$x = 2, y = 1$.
$3x + 4y = 10$ $...(1)$
$2x - 2y = 2$ $...(2)$
Multiplying equation $(2)$ by $2$,we obtain:
$4x - 4y = 4$ $...(3)$
Adding equation $(1)$ and $(3)$,we obtain:
$7x = 14$
$x = 2$ $...(4)$
Substituting $x = 2$ in equation $(1)$,we obtain:
$3(2) + 4y = 10$
$6 + 4y = 10$
$4y = 4$
$y = 1$
Hence,$x = 2, y = 1$.
By substitution method:
From equation $(2)$,we obtain:
$2x = 2 + 2y$
$x = 1 + y$ $...(5)$
Putting this value in equation $(1)$,we obtain:
$3(1 + y) + 4y = 10$
$3 + 3y + 4y = 10$
$7y = 7$
$y = 1$
Substituting the value $y = 1$ in equation $(5)$,we obtain:
$x = 1 + 1 = 2$
Therefore,$x = 2, y = 1$.
Explore More
Similar Questions
On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent:
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$
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 following pair of linear equations are consistent or inconsistent.
$5x - 3y = 11$; $-10x + 6y = -22$
$5x - 3y = 11$; $-10x + 6y = -22$
Easy
View SolutionForm 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 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 SolutionSolve the following pair of equations by reducing them to a pair of linear equations:
$\frac{1}{3x+y} + \frac{1}{3x-y} = \frac{3}{4}$
$\frac{1}{2(3x+y)} - \frac{1}{2(3x-y)} = -\frac{1}{8}$
$\frac{1}{3x+y} + \frac{1}{3x-y} = \frac{3}{4}$
$\frac{1}{2(3x+y)} - \frac{1}{2(3x-y)} = -\frac{1}{8}$
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