A pair of linear equations in two variables x and y is $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ , such that $\frac{a_{1}}{a_{2}} \neq \frac{c_{1}}{c_{2}}$ , then it has _______.

Unique solution

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No solution

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Infinitely many solutions

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Can't say

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Solution

The correct option is B Can't say
We are given the condition
$\frac{a_{1}}{a_{2}} \neq \frac{c_{1}}{c_{2}}$
As the relation with $b_{1}$ and $b_{2}$ isn't given, we can't say anything about the solutions of the equations and information about coefficients of $y$ is required.

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Similar questions

Unique point is obtained for the pair of equations $a_{1}$ x + $b_{1}$ y + $c_{1}$ = 0 and $a_{2}$ x + $b_{2}$ y + $c_{2}$ = 0 if __________ .

The condition for $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ to be consistent and have a unique solution is

If $a_{1} x + b_{1} y + c_{1} = 0, a_{2} x + b_{2} y + c_{2} = 0$ are two equations with an unique solution, then
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

$a_{1} x + b_{1} y + c_{1} = 0$ , $a_{2} x + b_{2} y + c_{2} = 0$ are two equations with no solutions , then $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Q. The condition for the pair of equations

a_{1} x + b_{1} y + c_{1} = 0

and

a_{2} x + b_{2} y + c_{2} = 0

to have a unique solution is -

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A pair of linear equations in two variables x and y is a1x+b1y+c1=0 and a2x+b2y+c2=0, such that a1a2≠c1c2, then it has _______.

The correct option is B Can't sayWe are given the conditiona1a2≠c1c2As the relation with b1 and b2 isn't given, we can't say anything about the solutions of the equations and information about coefficients of y is required.

A pair of linear equations in two variables x and y is $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ , such that $\frac{a_{1}}{a_{2}} \neq \frac{c_{1}}{c_{2}}$ , then it has _______.

The correct option is B Can't say
We are given the condition
$\frac{a_{1}}{a_{2}} \neq \frac{c_{1}}{c_{2}}$
As the relation with $b_{1}$ and $b_{2}$ isn't given, we can't say anything about the solutions of the equations and information about coefficients of $y$ is required.