Question

Identify the nature of the following pair of equations $-2x-3y+7=0,-6x-9y+21=0$.

• A. Both equations form intersecting line hence they have infinitely many solutions.
• B. Both equations form parallel line hence they have infinitely many solutions.
• C. Both equations form coincident line hence they have infinitely many solutions.
• D. None of these

Answer 1

The correct option is C Both equations form coincident line hence they have infinitely many solutions.

$-2x-3y+7=0......eq1and-6x-9y+21=\mathrm{0.........}eq2$
For many solution
$\frac{a_1}{b_1}=\frac{a_2}{b_2}=\frac{c_1}{c_2}$
here$\frac{-2}{-6}=\frac{1}{3}$
$\frac{b_1}{b_2}=\frac{-3}{-9}=\frac{1}{3}$
$\frac{c_1}{c_2}=\frac{7}{21}=\frac{1}{3}$
Hence $\frac{a_1}{b_1}=\frac{a_2}{b_2}=\frac{c_1}{c_2}$
thus the given pair of equation has many solution.