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

The value of k for which the system of equations \[\text{x}+\text{3y}-\text{3}=0\]and \[\text{4x}+\text{ky}+\text{7}=0\] has no solution, is:

A) 10

B) 7

C) 3

D) 12

Correct Answer: D

Solution :

[d] The given equations are \[x+3y-3=0\] and \[4x+ky+7=0.\].

Here, \[{{a}_{1}}=1,\,\,{{b}_{1}}=3,\,\,{{c}_{1}}=-3,\,\,{{a}_{2}}=4,\,\,{{b}_{2}}=k,\,\,{{c}_{2}}=7\]

The system of equations has no solution, if

\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\Rightarrow \frac{1}{4}=\frac{3}{k}\Rightarrow k=12\]