Question

The pair of equation x+2y+5=0 and -3x-6y+1=0 has

(a) a unique solution (b) exactly two solution

(c) infinitely many solutions (d) no solution

Answer 1

The given equations are

$x+2y+5=0$

$-3x-6y+1=0$

now,

$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

$a_1=1,b_1=2,b_1=5,\&$

$a_2=-3,b_2=-6,b_2=1,\&$

$\frac{a_1}{a_2}=\frac{1}{-3};\frac{b_1}{b_2}=\frac{2}{-6};\frac{c_1}{c_2}=\frac{5}{1}$

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

thus, the equations have no solution. i.e. system of given equations is in consistent.