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

Four years ago,the sum of the ages of a mother and her two daughters was $x$ years. What will be the sum of their ages after two years?

For the linear equation of two variables $ax + by + c = 0$,$\ldots \ldots \ldots \ldots$ is not true.

The cost of $5$ pants and $8$ shirts is ₹ $3100$. If the cost of a pant is ₹ $x$ and a shirt is ₹ $y$,then the linear equation in two variables is:

The pair of equations $5x - y = 9$ and $10x - 18 = 2y$ is $\ldots \ldots \ldots \ldots$

Solve the following pairs of equations:
$43x + 67y = -24$
$67x + 43y = 24$

Vedclass Test Series

Exam Paper Generator

Online Exam Module