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# Find the Value Of K For Which Each of the Following System of Equations Have No Solution : 2x + Ky = 11 5x − 7y = 5 - CBSE Class 10 - Mathematics

ConceptPair of Linear Equations in Two Variables

#### Question

Find the value of k for which each of the following system of equations have no solution :

2x + ky = 11
5x − 7y = 5

#### Solution

The given system of equation is

2x + ky - 11 =0

5x − 7y - 5 = 0

The system of equation is of the form

a_1x + b_1y + c_1 = 0

a_2x + b_2y + c_2 = 0

Where, a_1 = 2,b_1 = k, c_1 = -11

And a_2 = 5, b_2 = -7, c_2 = -5

For a unique solution, we must have

a_1/a_2 - b_1/b_2 != c_1/c_2

=> 2/5 = k/(-7) != (-11)/(-5)

Now

2/5 = k/(-7)

=> 2 xx (-7) = 5k

=> 5k = -14

=> k = (-14)/5

Cleary for (-14)/5 we have k/(-7) != (-11)/(-5)

Hence, the given system of equation will have no solution if k = (-14)/5

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Solution Find the Value Of K For Which Each of the Following System of Equations Have No Solution : 2x + Ky = 11 5x − 7y = 5 Concept: Pair of Linear Equations in Two Variables.
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