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
Hint:
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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