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?

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

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

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

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

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Solution

The correct option is A $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Given: Pair of linear equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ ( where $a_{1}, b_{1}, c_{1}, a_{2}, b_{2}, a n d c_{2}$ are all real numbers and $a_{1}, b_{1}, a_{2}, b_{2}$ are not equal to zero )

For, the two equations to be parallel, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ .
Hence, the correct answer is option (1).

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Q. If

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

and

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

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

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represents

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If the pair of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0,(a1,b1,c1,a2,b2 and c2 are all real numbers and a1,b1,a2,b2, are not equal to zero) represents parallel lines, then which of the following is correct?

The correct option is A a1a2=b1b2≠c1c2 Given: Pair of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0 ( where a1,b1,c1,a2,b2,and c2 are all real numbers and a1,b1,a2,b2 are not equal to zero ) For, the two equations to be parallel, a1a2=b1b2≠c1c2. Hence, the correct answer is option (1).

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?