On comparing the ratios frac{a_{1}}{a_{2}}, f | vedclass

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(C) Given equations are:$9x + 3y + 12 = 0$$18x + 6y + 24 = 0$Comparing these equations with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}

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Coincident

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(C) Given equations are:$9x + 3y + 12 = 0$$18x + 6y + 24 = 0$Comparing these equations with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,we get:$a_{1} = 9, b_{1} = 3, c_{1} = 12$$a_{2} = 18, b_{2} = 6, c_{2} = 24$Now,calculating the ratios:$\frac{a_{1}}{a_{2}} = \frac{9}{18} = \frac{1}{2}$$\frac{b_{1}}{b_{2}} = \frac{3}{6} = \frac{1}{2}$$\frac{c_{1}}{c_{2}} = \frac{12}{24} = \frac{1}{2}$Since $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$,the lines representing the given pair of equations are coincident,and there are infinitely many solutions.

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 pairs of linear equations intersect at a point,are parallel,or are coincident:
$9x + 3y + 12 = 0$
$18x + 6y + 24 = 0$

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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 pairs of linear equations intersect at a point,are parallel,or are coincident:$9x + 3y + 12 = 0$$18x + 6y + 24 = 0$