Which of the following pairs of linear equations are consistent/inconsistent? If consistent,obtain the solution graphically: $2x - 2y - 2 = 0, 4x - 4y - 5 = 0$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(B) Given equations are:
$2x - 2y - 2 = 0$ (Equation $1$)
$4x - 4y - 5 = 0$ (Equation $2$)
Comparing these with the standard form $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$,we get:
$a_1 = 2, b_1 = -2, c_1 = -2$
$a_2 = 4, b_2 = -4, c_2 = -5$
Now,find the ratios:
$\frac{a_1}{a_2} = \frac{2}{4} = \frac{1}{2}$
$\frac{b_1}{b_2} = \frac{-2}{-4} = \frac{1}{2}$
$\frac{c_1}{c_2} = \frac{-2}{-5} = \frac{2}{5}$
Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$,the lines are parallel to each other.
Therefore,the pair of linear equations is inconsistent and has no solution.

Explore More

Similar Questions

Form the pair of linear equations for the following problems and find their solution by the substitution method.
The coach of a cricket team buys $7$ bats and $6$ balls for ₹ $3800$. Later,she buys $3$ bats and $5$ balls for ₹ $1750$. Find the cost of each bat and each ball.

Difficult
View Solution

Solve the following pair of linear equations by the substitution method.
$s-t=3$
$\frac{s}{3}+\frac{t}{2}=6$

Difficult
View Solution

Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{5}{x-1} + \frac{1}{y-2} = 2$
$\frac{6}{x-1} - \frac{3}{y-2} = 1$

Formulate 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.

Which 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.
$2x + y = 5$
$3x + 2y = 8$

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo