10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

The pair of equations \[\text{x}+\text{2y}+\text{5=0}\]and \[-\text{3x}-\text{6y}+\text{1}=0\]have: (NCERT EXEMPLAR)

A) a unique solution

B) exactly two solutions

C) infinitely many solutions

D) no solution

Correct Answer: D

Solution :

[d] We have. \[x+2y+5=0\]

and \[-3x-6y+1=0\]

Here. \[{{a}_{1}}=1,\,{{b}_{1}}=2,\,{{c}_{1}}=5\]

and \[{{a}_{2}}=-3,\,{{b}_{2}}=-6,\,{{c}_{2}}=1\]

Now, \[\frac{{{a}_{1}}}{{{a}_{2}}}=-\frac{1}{3},\,\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{2}{-6}=-\frac{1}{3},\,\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{5}{1}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\]

So, the pair of equations have no solution.