Question

For what value of K, do the equations 2x-3y +10=0
and 3x+ky+15=0 to represent coincident lines.
a) - 9/2 (b) -11 (c) 9/2 (d)-7​

Answer 1

The value of k = - 9/2

Given :

The equations 2x - 3y + 10 = 0 and 3x + ky + 15 = 0

To find :

The value of k for which the equations 2x - 3y + 10 = 0 and 3x + ky + 15 = 0 represent coincident lines

(a) - 9/2

(b) - 11

(c) 9/2

(d) - 7

Concept :

A given pair of equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 represent coincident lines when

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

Solution :

Step 1 of 2 :

Write down the given pair of equations

Here the given pair of equations are

2x - 3y + 10 = 0 - - - - - - (1)

3x + ky + 15 = 0 - - - - - - (2)

Step 2 of 2 :

Find the value of k

2x - 3y + 10 = 0 - - - - - - (1)

3x + ky + 15 = 0 - - - - - - (2)

Comparing with the general equation a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 we get

a₁ = 2 , b₁ = - 3 , c₁ = 10 and a₂ = 3 , b₂ = k , c₂ = 15

Thus we get ,

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

$\displaystyle \sf{ \implies \frac{2}{3} = \frac{ - 3}{k} = \frac{10}{15} }$

$\displaystyle \sf{ \implies \frac{2}{3} = \frac{ - 3}{k} }$

$\displaystyle \sf{ \implies 2k = - 9}$

$\displaystyle \sf{ \implies k = - \frac{9}{2} }$

So the required value of k = - 9/2

Hence the correct option is (a) - 9/2

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