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

The pair of equations \[\text{5x-15y}=\text{8}\] and \[3x-9y=\frac{24}{5}\]has/have: (NCERT EXEMPLAR)

A) solution

B) two solutions

C) infinitely many solutions

D) no solution

Correct Answer: C

Solution :

[c] Given, \[5x-15y=8\] and \[3x-9y=\frac{24}{5}\]

Here, \[{{a}_{1}}=5,\,\,{{b}_{1}}=-15,\,\,{{c}_{1}}=8\]

and \[{{a}_{2}}=3,{{b}_{2}}=-9,{{c}_{2}}=\frac{24}{5}\]

\[\therefore \,\,\,\,\,\,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{5}{3},\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{-15}{-9}=\frac{5}{3}\]

and \[\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{8\times 5}{24}=\frac{5}{3}\]

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

which shows that the given equations have infinitely many solutions.