InterviewSolution
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InterviewSolution
| 1. |
If the lines 2x + y-3=0,5x+Ky-3=0 and 3x-y-2=0 are concurrent , find the value of K |
| Answer» We know that, Three lines are said to be concurrent, if they pass through a common point which also means that the point of intersection of any two lines always lies on the third line.Now, the three given equations of line are:2x + y − 3 = 0 ... (1)5x + ky − 3 = 0 ... (2)and 3x − y − 2 = 0 ... (3)Firstly, we will solve the equations (1) and (3) and find out the value of x and y. The corresponding value of x and y will also satisfy the equation (2) as all the given lines are concurrent.Therefore, on adding (1) and (3), we get2x + y − 3 + 3x − y − 2 = 0⇒ 5x - 5 = 0⇒ x = 1On putting value of x in (1), we get2(1) + y − 3 =0⇒ y - 1 = 0⇒ y = 1So, the point of intersection of two lines is (1, 1).Now, this point will also satisfy the equation (2).Therefore, on putting (x, y) = (1, 1) in (2), we get5(1) + k(1) − 3 = 0⇒ k + 2 = 0⇒ k = - 2\xa0 | |