Question 87

2x- ky + 7 = 0 and 6x- 12y+ 15 = 0 has no solution for

Solution

NOTE : - For the pair of equations : $$a_1x + b_1y + c_1 = 0$$ and $$a_2x + b_2y + c_2 = 0$$

The equations have no solution only if : $$\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$$

Equations : $$2x- ky + 7 = 0$$ and $$6x- 12y+ 15 = 0$$

Comparing with above formula, we get :

=> $$\frac{2}{6} = \frac{-k}{-12}$$

=> $$\frac{k}{12} = \frac{1}{3}$$

=> $$k = 4$$

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