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# Find the Value Of K For Which Each of the Following System of Equations Have Infinitely Many Solutions : 2x + 3y − 5 = 0 6x + Ky − 15 = 0 - CBSE Class 10 - Mathematics

ConceptPair of Linear Equations in Two Variables

#### Question

Find the value of k for which each of the following systems of equations has infinitely many solutions :

2x + 3y − 5 = 0
6x + ky − 15 = 0

#### Solution

The given system of equation is

2x + 3y − 5 = 0

6x + ky − 15 = 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 = 3, c_1 = -5

And a_2 = 6, b_2 = k,c_2 = -15

For a unique solution, we must have

a_1/a_2 = b_1/b_2 = c_1/c_2

=> 2/6 = 3/k

=> k = 18/2 = 9

Hence, the given system of equations will have infinitely many solutions, if k = 9.

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Solution Find the Value Of K For Which Each of the Following System of Equations Have Infinitely Many Solutions : 2x + 3y − 5 = 0 6x + Ky − 15 = 0 Concept: Pair of Linear Equations in Two Variables.
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