Question

state true or false and explain : The value of k for the equations 3x-y + 8 = 0 and 6x-ky + 6 = 0 represent coincident lines is 3

Answer 1

false because the value of k_-6

Answer 2

Answer:

Concept:

The value of k for the equations 3x-y + 8 = 0 and 6x-ky + 6 = 0 represent coincident lines is 3  : False

Step-by-step explanation:

Given:

The equations are

               $\begin{aligned}&3 x-y+8=0 \\&6 x-k y+6=0\end{aligned}$

Find:

The value of k in the given equations.

Solution:

Here, $\mathrm{a}_{1}=3, \mathrm{~b}_{1}=-1, \mathrm{c}_{1}=8$

and    $a_{2}=6, b_{2}=-k, c_{2}=6$

The equation will represent coincident lines only when they have infinite number of solutions.

                           $\frac{\mathrm{a}_{1}}{\mathrm{a}_{2}}=\frac{\mathrm{b}_{1}}{\mathrm{~b}_{2}}=\frac{\mathrm{c}_{1}}{\mathrm{c}_{2}}$

$\\Taking, \frac{3}{6}=\frac{-1}{-\mathrm{k}} \Rightarrow \frac{1}{2}=\frac{1}{\mathrm{k}} \Rightarrow \mathrm{k}=2$

Taking,

$\\Taking, \frac{8}{6}=\frac{-1}{-\mathrm{k}} \Rightarrow \frac{4}{3}=\frac{1}{\mathrm{k}} \Rightarrow \mathrm{k}=3$

Hence the value of k is 3 and 2 .

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