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# Find the Value Of K For Which Each of the Following Systems of Equations Has Infinitely Many Solutions : 4x + 5y = 3 Kx + 15y = 9 - 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 :

4x + 5y = 3

kx + 15y = 9

#### Solution

The given system of equation is

4x + 5y -3 = 0

ks + 15y - 9 = 0

The system of equation is of the for

a_1x + b_1y + c_1= 0

a_2x + b_2y + c_2 = 0

Where a_1 = 4, b_1 = 5, c_1 = -3

And a_2 = k, b_2 = 15, c_2 = -9

For a unique solution, we must have

a_1/a_2 = b_1/b_2 = c_2/c_2

=> 4/k = 5/15 = (-3)/(-9)

Now

4/k = 5/15

=> 4/k = 1/3

=> k = 12

Hence, the given system of equations will have infinitely many solutions, if k = 12

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Solution Find the Value Of K For Which Each of the Following Systems of Equations Has Infinitely Many Solutions : 4x + 5y = 3 Kx + 15y = 9 Concept: Pair of Linear Equations in Two Variables.
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