 Hello and welcome to the session. In this session we will discuss a question which says that for what value of m are the three lines 3x plus 4y is equal to 7, x minus y plus 2 is equal to 0 and y is equal to mx plus 2 are concurrent. Now before starting the solution of this question we should know a result and that is three lines are said to be concurrent if point of intersection two lines lie on the third line 2. Or we can say the three lines are concurrent if they meet the point that is they have a common point of intersection. Now this result will work out as a key idea for solving out this question. And now we will start with the solution. First we will find the point of intersection of these two lines. So the equations are given as 3x plus 4y is equal to 7 and x minus y plus 2 is equal to 0. Now these equations can also be written as 3x plus 4y is equal to 7 and x minus y is equal to minus 2. Let us name this as 1 and this as 2. Now we will solve equation number 1 and 2 simultaneously and for this multiply equation number 2 by 3. This implies 3x plus 4y is equal to 7 and 3x minus 3y is equal to minus 6. Let us name it as 3 and this as 4. Now subtracting equation number 4 from 3 we get 3x plus 4y within brackets minus 3x minus 3y within brackets is equal to 7 minus of minus 6. This implies 3x plus 4y minus 3x plus 3y is equal to 7 plus 6. This implies 3x will be cancelled with 3x and here it will be 7y is equal to 7 plus 6 which is 13. Further this implies y is equal to 13 by 7. Now putting y is equal to 13 by 7 in equation number 2 we get x minus 13 by 7 is equal to minus 2. This implies x is equal to minus 2 plus 13 by 7. This implies x is equal to minus 14 plus 13 whole upon 7. Further this implies x is equal to minus 1 by 7. Therefore the point of intersection of the two lines is minus 1 by 7, 13 by 7. Now given these three lines are concurrent that means the point of intersection of the first two lines will lie on the third line too. Now given the lines are concurrent therefore the point of intersection of the first two lines which is minus 1 by 7, 13 by 7 will lie on the third line which is y is equal to mx plus 2. This implies 30 by 7 is equal to m into minus 1 by 7 plus 2. Further this implies 30 by 7 is equal to minus m by 7 plus 2. This implies 30 by 7 is equal to minus m plus 14 whole upon 7. Further this implies now where 7 will be cancelled with 7 so 13 is equal to minus m plus 14. Now this implies m is equal to 14 minus 13 which implies m is equal to 1. Hence the required value of m is equal to 1. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed the session.