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 parallel lines.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) For two lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to be parallel,the condition is $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$.
Given the equation $2x + 3y - 8 = 0$,we have $a_1 = 2, b_1 = 3, c_1 = -8$.
To satisfy the condition,we can choose $a_2 = 4$ and $b_2 = 6$ (which makes $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{1}{2}$) and choose $c_2$ such that $\frac{c_1}{c_2} \neq \frac{1}{2}$.
Let $c_2 = -10$. Then the equation is $4x + 6y - 10 = 0$.
Checking the condition: $\frac{2}{4} = \frac{3}{6} \neq \frac{-8}{-10}$,which simplifies to $\frac{1}{2} = \frac{1}{2} \neq \frac{4}{5}$.
Thus,$4x + 6y - 10 = 0$ is a valid answer.

Explore More

Similar Questions

Solve the following pair of equations by reducing them to a pair of linear equations:
$\frac{4}{x} + 3y = 14$
$\frac{3}{x} - 4y = 23$

Solve the following pair of linear equations by the elimination method and the substitution method:
$3x + 4y = 10$ and $2x - 2y = 2$

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

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.

Solve the following pair of linear equations:
$(a-b)x + (a+b)y = a^2 - 2ab - b^2$
$(a+b)(x+y) = a^2 + b^2$

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