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Byju's Answer

Standard IX

Mathematics

Inconsistent Equation

In the pair o...

Question

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?

S1 only

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S1 and S2

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S1 and S3

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S2 only

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Solution

The correct option is C
S1 and S3

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

if $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ , then the lines representing these equations are parallel.

Hence, there will be no solution and the pair of equations will be inconsistent.

$∴$ Statements 1 and 3 are correct.

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Similar questions

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 ?

State whether the given statement is true or false:

A pair of linear equations is given by

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

and

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

and

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

In this case, the pair of linear equations is inconsistent.

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

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?

Q. STATEMENT - 1 :

\sqrt{2} x + \sqrt{3} y = 0, \sqrt{3} x - \sqrt{8} y = 0

has no solution.
STATEMENT - 2 : If a pair of linear equations is given by

a_{1} x + b_{1} y + c_{1} = 0, a_{2} x + b_{2} y + c_{2} = 0

and

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

.
In this case, the pair of linear equations is consistent.

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In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0, a1a2=b1b2≠c1c2 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 correct option is C S1 and S3 In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0, if a1a2=b1b2≠c1c2, then the lines representing these equations are parallel. Hence, there will be no solution and the pair of equations will be inconsistent. ∴ Statements 1 and 3 are correct.