In the pair of linear equations a_{1}x + b_{1 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a pair of linear equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$:$1$. If $\frac{a_{1}}{a_{2}} 
eq \frac{b_{1}}{b_{2

Vedclass · Accepted Answer

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

Vedclass · Answer

(C) For a pair of linear equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$:$1$. If $\frac{a_{1}}{a_{2}} 
eq \frac{b_{1}}{b_{2}}$,the lines intersect at a single point,resulting in a unique solution.$2$. If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} 
eq \frac{c_{1}}{c_{2}}$,the lines are parallel,resulting in no solution.$3$. If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$,the lines are coincident,meaning they overlap at every point,resulting in infinitely many solutions.Therefore,the condition for infinitely many solutions is $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$.

In the pair of linear equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,if $\ldots \ldots \ldots \ldots$,then the system has infinitely many solutions.

Similar Questions

Are the following pair of linear equations consistent? Justify your answer.
$\frac{3}{5} x - y = \frac{1}{2}$
$\frac{1}{5} x - 3 y = \frac{1}{6}$

$x=-1$ and $y=-2$ is one of the solutions of the equation $\ldots \ldots \ldots \ldots$

If the following pair of equations is consistent (unique solution),then find the value of $k$:
$x - ky = 2$
$3x + 2y = -5$

The sum of two numbers is $8$. If the smaller number is $y$,then the larger number $x = \ldots \ldots \ldots \ldots$

Solve the following pairs of equations by the cross-multiplication method:
$0.5x + 0.3y = 0.1$
$0.6x + 0.3y = 0.3$

Vedclass Test Series

Exam Paper Generator

Online Exam Module