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

The system of linear equations representing both the situations will have

A) unique solution

B) no solution

C) infinitely many solutions

D) None of the above

Correct Answer: A

Solution :

Here, \[{{a}_{1}}=1,\,{{b}_{1}}=5,\,{{c}_{1}}=450\]

and \[{{a}_{2}}=1,\,{{b}_{2}}=10,\,{{c}_{2}}=850\]

\[\frac{{{a}_{1}}}{{{a}_{2}}}=1,\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{5}{10}=\frac{1}{2},\,\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{450}{850}=\frac{9}{17}\]

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

Hence, unique solutions.