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, do the equations \[\text{3x}-\text{y}+\text{8}=0\]and \[\text{6x}-k\text{y}=-\text{16}\] represent coincident lines? (NCERT EXEMPLAR)

A) \[1/2\]

B) \[-1/2\]

C) \[2\]

D) \[-2\]

Correct Answer: C

Solution :

[c] Given equations of lines are \[3x-y+8=0\]

and \[6x-ky+16=0\]

Here, \[{{a}_{1}}=3,\,{{b}_{1}}=-1,\,{{c}_{1}}=8\]

and \[{{a}_{2}}=6,\,\,{{b}_{2}}=-k,\,{{c}_{2}}=16\]

These equations represent coincident lines if

\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\Rightarrow \frac{3}{6}=\frac{-1}{-k}=\frac{8}{16}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\frac{1}{k}=\frac{1}{2}\Rightarrow k=2\]