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find the value of k for which the given system of equation have a unique solution 4x-5y=k 2x-3y=12 |
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Answer» Step-by-step explanation:The given SYSTEM of equations are 4x - 5y = k ⇒ 4x - 5y - k = 0(i) And, 2x - 3y = 12 ⇒2x - 3y - 12 = 0 …(ii) These equations are of the following form: a1x+b1y+c1 = 0 a2x+b2y+c2 = 0 Here, a1 = 4, B1= -5, c1 = -k and A2 = 2, b2 = -3, c2 = -12 For a UNIQUE solution, we must have: a1/a2 not equal to b1/b2ie. 4/2 is not equal to -5/-3which implies; 2 is not equal to 5/3and 6 is not equal to 5Thus, for all real values of k, the given system of equations will have a unique solution. |
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