Choose the correct answer from the given four options:The pair of equations $x+2 y+5=0$ and $-3 x-6 y+1=0$ have(A) a unique solution(B) exactly two solutions(C) infinitely many solutions(D) no solution

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Given:

Given pair of linear equations is:

$x+2 y+5=0$ and $-3 x-6 y+1=0$

To do:

We have to find the correct option.

Solution:

Comparing the given pair of linear equations with the standard form of linear equations $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$, we get,

$a_1=1, b_1=2$ and $c_1=5$

$a_2=-3, b_2=-6$ and $c_2=1$

Here,

$\frac{a_1}{a_2}=\frac{1}{-3}=-\frac{1}{3}$

$\frac{b_1}{b_2}=\frac{2}{-6}=-\frac{1}{3}$

$\frac{c_1}{c_2}=\frac{5}{1}$

$\frac{a_1}{a_2} = \frac{b_1}{b_2} ≠ \frac{c_1}{c_2}$

Therefore, the given pair of equations has no solution.

Updated on 10-Oct-2022 13:27:10