On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ find out whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident:
$x + 2 y = 8; 5 x - 10 y = 10$

Parallel

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Concident

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Intersect at a point

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None of these

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Solution

The correct option is A Intersect at a point
The equations are
$x + 2 y - 8 = 0$
$\Rightarrow a_{1} = 1, b_{1} = 2, c_{1} = - 8$
and $5 x - 10 y - 10 = 0$
$\Rightarrow a_{2} = 5, b_{2} = - 10, c_{2} = - 10$
Comparing $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$
$\frac{a_{1}}{a_{2}} = \frac{1}{5}$
$\frac{b_{1}}{b_{2}} = \frac{2}{- 10} = \frac{1}{- 5}$
$\Rightarrow \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Hence,the lines representing the given pair of equations has a unique solution.
Thus the pair of lines intersect at a point.

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On comparing the ratios a1a2,b1b2 and c1c2 find out whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident:x+2y=8;5x−10y=10

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ find out whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident:
$x + 2 y = 8; 5 x - 10 y = 10$