STATEMENT -1 : $3 x + 2 y = 5, 2 x - 3 y = 7$ are consistent pair of equation.
STATEMENT - 2: If the 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 $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ .
In this case, the pair of linear equations is consistent.

Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

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Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

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Statement - 1 is True, Statement - 2 is False

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Statement - 1 is False, Statement - 2 is True

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Solution

The correct option is C Statement - 1 is True, Statement - 2 is False
For equations $S_{1} : \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ and hence the pair of lines will be consistent.
If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ , then there will not be any solution and hence the system of equations will be inconsistent.

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Similar questions

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.

Q. Statement

- 1 :

0 < x < y \Rightarrow {log}_{a} x > {log}_{a} y

, where

a > 1

.
Statement

- 2 :

When

a > 1, {log}_{a} x

is an increasing function.

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?

Q. Statement-1:

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} = (n + 2) 2^{n - 1} .

Statement-2:

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} x^{r} = (1 + x)^{n} + n x (1 + x)^{n - 1} .

Q. Statement-1:

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} = (n + 2) 2^{n - 1} .

Statement-2:

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} x^{r} = (1 + x)^{n} + n x (1 + x)^{n - 1} .

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STATEMENT -1 : 3x+2y=5,2x−3y=7 are consistent pair of equation.STATEMENT - 2: If the pair of linear equations is given by a1x+b1y+c1=0,a2x+b2y+c2=0 and a1a2=b1b2=c1c2.In this case, the pair of linear equations is consistent.

The correct option is C Statement - 1 is True, Statement - 2 is FalseFor equations S1:a1a2≠b1b2≠c1c2 and hence the pair of lines will be consistent.If a1a2=b1b2=c1c2, then there will not be any solution and hence the system of equations will be inconsistent.