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in Linear Equations by (49.1k points)
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If the equations 4x + 7y = 10 and 10x + ky = 25 represent coincident lines, then the value of k is:

(a) 5

(b) \(\frac{17}2\)

(c) \(\frac{27}2\)

(d) \(\frac{35}2\)

1 Answer

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by (48.0k points)
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Best answer

Correct option is (d) \(\frac{35}2\)

The given linear equation is

4x + 7y − 10 = 0

10x + ky − 25 = 0

Here a1​ = 4, b1​ = 7, c1​ = −10

and a2 ​= 10, b2 ​= k, c2​ = −25

\(\therefore \frac{a_1}{a_2} = \frac 4{10} = \frac 25\)

\(\frac{b_1}{b_2} = \frac 7k\)

\(\frac{c_1}{c_2} = \frac{-10}{-25} = \frac 25\)

If a linear equation represents a coincident lines then

\(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)

Then \(\frac 7k = \frac 25\)

\(\therefore k = \frac{35}2\) 

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