 Hello and welcome to the session. In this session we will discuss a question which says that find the equation of the line joining the points of intersection of 2x plus y is equal to 4 when x minus y plus 1 is equal to 0 and 2x minus y minus 1 is equal to 0 with x plus y minus 8 is equal to 0. Now before starting the solution of this question we should know a result. And that is the two points form. The equation of the straight line passing through the points x1 y1 and x2 y2 is y minus y1 is equal to y2 minus y1 over x2 minus x1 into x minus x1 the vote where slope m is equal to y2 minus y1 over x2 minus x1. Now this result will work out as a key idea for solving out this question. And now we will start with the solution. Firstly we have to find the point of intersection of these two lines. Now given the equation is 2x plus y is equal to 4 and x minus y plus 1 is equal to 0. Let us name it as 1 and this as 2. Now adding 1 and 2 we get 2x plus y plus x minus y plus 1 is equal to 4 plus 0. Now this implies here y will be cancelled with y so it will be 3x plus 1 is equal to 4. This implies 3x is equal to 4 minus 1 which implies 3x is equal to 3. Now this implies x is equal to 1. Now putting x is equal to 1 in equation number 1 we get 2 into 1 plus y is equal to 4. Now this implies 2 plus y is equal to 4. Further this implies y is equal to 4 minus 2. This implies y is equal to 2. Therefore the point of intersection of the lines 1 and 2 is 1, 2. Now we have to find the point of intersection of these two lines. Now given the equation of line s 2x minus y minus 1 is equal to 0 and x plus y minus 8 is equal to 0. Let us name it as 3 and this as 4. Now adding 3 and 4 we get 2x minus y minus 1 plus x plus y minus 8 is equal to 0. This implies here y will be cancelled with y so it will be 3x minus 9 is equal to 0. Which implies 3x is equal to 9. This implies on dividing both sides by 3 it will be x is equal to 3. Now putting x is equal to 3 in equation number 4 we get 3 plus y minus 8 is equal to 0. This implies y minus 5 is equal to 0. Which implies y is equal to 5. Therefore the point of intersection of the line 3 and 4 is 3 5. Now we have to find the equation of line joining the points of intersection that are 1, 2 and 3 5. Now we can find out the equation of the line by using this formula. Now let us take the point 1 2 as x 1 y 1 and the point 3 5 as x 2 y 2. Then the equation of the line by using the formula y minus y 1 is equal to y 2 minus y 1 over x 2 minus x 1 into x minus x 1 the whole. Now putting the values of x 1 y 1 and x 2 y 2 here this implies y minus 2 is equal to 5 minus 2 over 3 minus 1 into x minus 1 the whole. Which implies y minus 2 is equal to 3 by 2 into x minus 1 the whole. On cross multiplying this implies y minus 4 is equal to 3 x minus 3. This implies 3 x minus 2 y plus 1 is equal to 0. So this is the required equation of the line. So this is the solution of the given question and that is all for this session. Hope you all have enjoyed the session.