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

For what value of p, do the equations \[-\text{3x}+\text{5y}=\text{7}\]and \[\text{2px}-\text{3y}=\text{1}\]represent intersecting lines? (NCERT EXEMPLAR)

A) All real values of p except \[\frac{9}{10}\]

B) All real values of p

C) All real values of p except \[\frac{10}{9}\]

D) None of the above

Correct Answer: A

Solution :

[a] Given, \[-3x+5y=7\]and \[2px-3y=1\]

Here, \[{{a}_{1}}=-3,\,\,{{b}_{1}}=5,\,\,{{c}_{1}}=7\]

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

Condition for intersecting lines, \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\frac{-3}{2p}\ne \frac{5}{-3}\Rightarrow p\ne \frac{9}{10}\]

\[\therefore \,\,\,\,\,\,\,\,p\in R-\left\{ \frac{9}{10} \right\}\]