The system kx y 2 and 6x 2y 3 has a unique solution when *
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Correct Answer = (d) k ≠ 3 Show The given equations are kx – y – 2 = 0 ………(i) 6x – 2y – 3 = 0 ……..(ii) Here, a1 = k, b1 = -1, c1 = -2, a2 = 6, b2 = -2 and c2 = -3. For the given system to have a unique solution, we must have kx – y – 2 = 0 ……(i) 6x – 2y – 3 = 0 ……(ii) Here, `a_1 = k, b_1 = -1, c_1 = -2, a_2 = 6, b_2 = -2 and c_2 = -3` For the system, to have a unique solution, we must have `(a_1)/(a_2) ≠ (b_1)/(b_2)` `⇒ k/6 ≠ (−1)/(−2) = 1/2` ⇒ k ≠ 3 Hence, k ≠ 3. When the system of equation has a unique solution the system is?Systems of equations can be classified by the number of solutions. If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent .
What is the value of k if the system of equations kx y 2 and 6x 2y 3 have infinitely many solutions?∴ For unique solution of system of equations, k=3,4.
For what value of k equation has unique solution?So, the given of equations system will have a unique solution, if k=3.
What type of system has a unique solution?An independent system has exactly one solution pair (x,y) . The point where the two lines intersect is the only solution.
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