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

For what value of k does the pair of equations \[\text{x}-\text{2y}=\text{3}\]and \[\text{2x}+\text{ky}=5\] have a unique solution?

A) \[k=-4\]

B) \[k=0\]only

C) \[k\ne -1\]

D) \[k\ne -4\]

Correct Answer: D

Solution :

[d] The given pair of linear equation is

\[x-2y-3=0\] and \[2x+ky-5=0\]

For unique solution: \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\frac{1}{2}\ne \frac{-2}{k}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,k\ne -4\]