Graphically,find whether the following pair of equations has no solution,unique solution or infinitely many solutions.
$5x - 8y + 1 = 0$ $...(1)$
$3x - \frac{24}{5}y + \frac{3}{5} = 6$ $...(2)$

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) Given equations are:
$5x - 8y + 1 = 0$ $...(1)$
$3x - \frac{24}{5}y + \frac{3}{5} = 6$ $...(2)$
Multiply Equation $(2)$ by $\frac{5}{3}$:
$\frac{5}{3} \times (3x - \frac{24}{5}y + \frac{3}{5}) = \frac{5}{3} \times 6$
$5x - 8y + 1 = 10$
Wait,let us re-examine Equation $(2)$ as given: $3x - \frac{24}{5}y + \frac{3}{5} = 6$.
Multiplying by $\frac{5}{3}$ gives $5x - 8y + 1 = 10$,which simplifies to $5x - 8y - 9 = 0$.
Comparing $5x - 8y + 1 = 0$ and $5x - 8y - 9 = 0$,the coefficients of $x$ and $y$ are the same,but the constants are different.
Therefore,the lines are parallel and have no solution.

Explore More

Similar Questions

The students of a class are made to stand in rows. If $3$ students are extra in a row,there would be $1$ row less. If $3$ students are less in a row,there would be $2$ rows more. Find the number of students in the class.

Difficult
View Solution

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.
$3x + 2y = 5; \quad 2x - 3y = 7$

$A$ boat goes $30\, km$ upstream and $44\, km$ downstream in $10\, hours.$ In $13\, hours,$ it can go $40\, km$ upstream and $55\, km$ downstream. Determine the speed of the stream and that of the boat in still water.

Difficult
View Solution

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 coincident lines.

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.
$2x - 3y = 8$; $4x - 6y = 9$

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