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

Find the value of k for which the system of equations \[\text{x}+\text{3y}=\text{4}\]and \[\text{3x}+\text{ky}+\text{12}=0\] are inconsistent.

A) \[k=12\]

B) \[k=-12\]

C) \[k=9\]

D) \[k=-9\]

Correct Answer: C

Solution :

[c] The given equations are

\[x+3y-4=0\] and \[3x+ky+12=0\]

Here, \[{{a}_{1}}=1,\,{{b}_{1}}=3,\,{{c}_{1}}=-4,\,{{a}_{2}}=3,{{b}_{2}}=k,\,{{c}_{2}}=12\]

For inconsistent equations:

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

\[\Rightarrow \,\,\,\,\,\,k=9\]and \[k\ne -9\]