Question

The pair of equations $x+2y+5=0$ and $-3x-6y+1=0$ have

• A. A unique solution
• B. Exactly two solutions
• C. Infinitely many solutions
• D. No solution

Answer 1

Answer: (D)

No solution

The given equations are:
$x+2y+5=0$
$-3x-6y+1=0$
From the given equations we have:
$\frac{a_1}{a_2}=\frac{1}{-3}$
$\frac{b_1}{b_2}=\frac{2}{-6}=\frac{1}{-3}$
$\frac{c_1}{c_2}=\frac{5}{1}$
$\Rightarrow \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
Hence the given pair of equations have no solution.