Determine the number of solutions for the given pair of linear equations in two variables:
x + 2y + 5 = 0 and -3x – 6y + 1 = 0

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Solution

Given are x + 2y + 5 = 0 and -3x - 6y + 1 = 0
$H e r e, a_{1} = 1, b_{1} = 2, c_{1} = 5 a n d a_{2} = - 3, b_{2} = - 6, c_{2} = 1 \frac{a_{1}}{a_{2}} = - \frac{1}{3} \frac{b_{1}}{b_{2}} = - \frac{2}{6} = - \frac{1}{3} \frac{c_{1}}{c_{2}} = \frac{5}{1} \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
Hence, the pair of equations has no solution.

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