Question

If Kx + 3y - 5 =0 and 3x + 9y - 15 = 0 represents coincident lines, then find the value of K
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Answer 1

Answer:

Step-by-step explanation:

The given system may be written as

kx + 3y − 5 = 0  

3x + 9y − 15 = 0

The given system of equation is of the form

a1x + b1y − c1 = 0  

a2x + b2y − c2 = 0  

Where, a1 = k, b1 = 3, c1 = −5

a2 = 3, b2 = 9, c2 = −15

For unique solution, we have

$\frac{a1}{a2}$ =  $\frac{b1}{b2}$ = $\frac{c1}{c2}$

$\frac{k}{3}$ = $\frac{3}{9}$ = $\frac{-5}{-15}$

$\frac{k}{3}$ = $\frac{3}{9}$                       OR                  $\frac{k}{3}$ = $\frac{-5}{-15}$  

            By cross multiplication

9k = 9                                     -15k = -15

  k = $\frac{9}{9}$                                          k = $\frac{-15}{-15}$

  k = 1                                          k = 1

Therefore, the given equation has infinitely many solution.

And the value of k is 1.

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