If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ in the system of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$

S1 : The following is condition for inconsistent equations

S2 : There exists infinitely many solutions

S3 : The equations satisfying the condition are parallel

Which of the following statements are true ?

S1 only

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S1 and S2

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S1 and S3

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All are true

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Solution

The correct option is C
S1 and S3

For two lines $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ ,
If they satisfy, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ , then the equations are inconsistent and the lines representing them are parallel.

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Similar questions

In the pair of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ ,

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

Statement 1 : This is an inconsistent pair of linear equations.

Statement 2 : There exists infinitely many solutions.

Statement 3 : The lines representing these linese are parallel.

Which of the above statements is/are true?

The condition for a pair of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ to be parallel is

Parallel lines are 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

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

Q. If the pair of linear equations

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

and

a_{2} x + b_{2} y + c_{2} = 0, (a_{1}, b_{1}, c_{1}, a_{2}, b_{2} a n d c_{2}

are all real numbers and

a_{1}, b_{1}, a_{2}, b_{2},

are not equal to zero) represents parallel lines, then which of the following is correct?

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If a1a2=b1b2≠c1c2 in the system of equations a1x+b1y+c1=0 and a2x+b2y+c2=0 S1 : The following is condition for inconsistent equations S2 : There exists infinitely many solutions S3 : The equations satisfying the condition are parallel Which of the following statements are true ?

The correct option is C S1 and S3 For two lines a1x+b1y+c1=0 and a2x+b2y+c2=0, If they satisfy, a1a2=b1b2≠c1c2, then the equations are inconsistent and the lines representing them are parallel.

The correct option is C
S1 and S3

For two lines $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ ,
If they satisfy, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ , then the equations are inconsistent and the lines representing them are parallel.