Question

wo value of
For what values of k' do the equations
3x-y +8=0 and
-o and 6x - xy = 16 represent coincident
lines.​

Answer 1

SOLUTION

GIVEN

Two lines 3x - y + 8 = 0 and 6x - ky + 16 = 0 represents coincident lines

TO DETERMINE

The value of k

CONCEPT TO BE IMPLEMENTED

For the given two linear equations

$\displaystyle \sf{ a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0}$

Consistent :

One of the Below two condition is satisfied

1. Unique solution :

$\displaystyle \sf{ \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2} }$

2. Infinite number of solutions ( Coincident lines) :

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} = \: \frac{c_1}{c_2}}$

Inconsistent :

No solution

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \: \frac{c_1}{c_2}}$

EVALUATION

Here the given equation of the lines are

3x - y + 8 = 0 and 6x - ky + 16 = 0

Now the given lines are coincident

Thus we get

$\displaystyle \sf{ \frac{3}{6} = \frac{ - 1}{ - k} = \frac{8}{16} }$

$\displaystyle \sf{ \implies \: \frac{1}{2} = \frac{ 1}{ k} }$

$\displaystyle \sf{ \implies k = 2}$

Hence the required value of k = 2

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