Question

Question 2
The pair of equation x + 2y + 5 = 0 and -3x – 6y + 1 = 0 has
(A) a unique solution
(B) exactly two solutions
(C) infinitely many solutions
(D) no solution

Answer 1

Given are x + 2y + 5 = 0 and -3x - 6y + 1 = 0
$Here,a_1=1,b_1=2,c_1=5and{a}_2=-3,b_2=-6,c_2=1\frac{a_1}{a_2}=-\frac{1}{3}\frac{b_1}{b_2}=-\frac{2}{6}=-\frac{1}{3}\frac{c_1}{c_2}=\frac{5}{1}\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
Hence, the pair of equations has no solution.