Maths-
General
Easy

Question

In the following system of linear equations, k is a constant and x and y are variables. For what value of k will the system of equations have infinitely many solution?
kx - 3y = 12
4x - 5y = 20

hintHint:

1. When Both sides of an equation are equal, the said equation is said to have infinitely many solutions.
i.e. When LHS = RHS, the given equation has infinitely many solutions.
2. For Equations with Infinitely Many solutions:-
(a1/a2) = (b1/b2) = (c1/c2)

The correct answer is: For k = 2.4, the given set of equations will have Infinitely Many Solutions.


    Step-by-step solution:-
    From the given information, we have-
    kx - 3y = 12 ….................................................. (Equation i)
    4x - 5y = 20 ….................................................. (Equation ii)
    Comparing the above equations with standard form of equations i.e. ax + by = c, we get-
    a1 = k, b1 = -3, c1 = 12
    a2 = 4, b2 = -5, c2 = 20
    We know that for Equations with no solution-
    (a1/a2) = (b1/b2) = (c1/c2)
    i.e. k/4 = -3/-5 = 12/20 .................................................. (Equation iii)
    ∴ k/4 = -3/-5 ........................................................................... (From Equation iii)
    ∴ k/4 = 3/5
    ∴ 5k = 4 * 3 .......................................................................... (Cross multiplying)
    ∴ 5k = 12
    ∴ k = 12/5
    ∴ k = 2.4
    Final Answer:-
    ∴ For k = 2.4, the given set of equations will have Infinitely Many Solutions.

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