 Hello and welcome to the session. Let us discuss the following question. It says, find the value of p so that the three lines 3x plus y minus 2 is equal to 0, px plus 2y minus 3 is equal to 0 and 2x minus y minus 3 is equal to 0 may intersect at one point. Let us now move on to the solution. The lines given to us are 3x plus y minus 2 is equal to 0, px plus 2y minus 3 is equal to 0, 2x minus y minus 3 is equal to 0. Now we are given that the three lines intersect at one point. So we first find the point of intersection of the lines. So we solve equation 1 and 3 since the value of p is not known to us, we cannot solve equation 2 with any of the equations. So we solve equation 1 and 3. Equation 1 is 3x plus y minus 2 is equal to 0 and equation 3 is 2x minus y minus 3 is equal to 0. Now we add equation 1 and 3 when we add plus y gets cancelled with minus y, 3x plus 2x is 5x minus 2 minus 3 is minus 5 is equal to 0. So this implies 5x minus 5 is equal to 0, this implies x is equal to 1. Now put x is equal to 1 in equation 1. So we have 3 into 1 plus y minus 2 is equal to 0. So this implies y is equal to minus 1. So point of intersection of 1 and 3, 1 minus 1. Now we are given that the three lines intersect at one point and we have obtained the point of intersection of line 1 and 3 as 1 minus 1 therefore second line also passes through the point 1 minus 1 that means the point 1 minus 1 satisfies the equation of line given by 2. So put x is equal to 1 and y is equal to minus 1 in equation 2. Now equation 2 implies px 2y minus 3 is equal to 0. So this becomes p plus 2 into minus 1 is minus 2, minus 3 is equal to 0 and this implies p minus 5 is equal to 0 and this implies p is equal to 5. Hence our answer is 5. So this completes the question. Hope you enjoyed this session. Goodbye and take care.