 Hello and welcome to the session and it is not the following problem today. Is the following pair of linear equations consistent or inconsistent? If consistent obtain the solution graphically, we have x plus y is equal to 5 and 2x plus 2y is equal to 10. Now, the key idea first, the system of linear equations a1x plus b1y plus a1 is equal to 0 and a2x plus b2y is equal to 0 are consistent if a1 by a2 is not equal to b1 by b2 which is unique solution intersecting. Is inconsistent if a1 by a2 is equal to b1 by b2 is equal to c1 by c2 that is many solutions coincident. Is inconsistent if a1 by a2 is equal to b1 by b2 is not equal to c1 by c2. Now, let us write our solution given to us that x plus y is equal to 5 and 2x plus 2y is equal to 10. The given system of equations can be written as plus y minus 5 is equal to 0 2x plus 2y minus 10 is equal to 0 plus c1 is equal to 0 2y plus c2 is equal to 0 we get is equal to 1 b1 is equal to 1 c1 is equal to minus 5 and a2 is equal to 2 b2 is equal to 2 and c2 is equal to minus 10 a1 by a2 is equal to half b2 is equal to half and c1 by c2 is equal to minus 5 by minus 10 which is equal to half. Therefore, we can see that a1 by a2 is equal to b1 by b2 is equal to c1 by c2 which is equal to half. Therefore, the key idea equal to b1 by b2 is equal to c1 by c2 then given pair of equations given equations are of the graph we find the values of x and y. First we have plus y is equal to 5 plus 2y is equal to 10 x plus y is equal to 5. Now, writing the values we get for x is equal to 0 y is equal to 5 and for x is equal to 6 we get y is equal to 1. Here we can see both of the equation are same but we will be using the different values. So, for x is equal to 2 we get y is equal to 3 and for x is equal to 8 we get y is equal to minus 3. Let us plot the point 0.5 6 comma minus 1, 2 comma 3 and 8 comma minus 3 on a separate graph sheet. Let us see how a graph paper. So, now first plotting 0.5 taking 0 on x axis and taking 5 on y axis therefore, we get of this point as 0.5. Let us name it as a. We plotting the point 6 comma minus 1 taking 6 on x axis and minus 1 on y axis we get this point as our 6 comma minus 1 and naming it as 3. Now joining a b. Now let us join a b. Now we have joined a b and this is our required line x plus y is equal to 5. Now similarly plotting the points 2 comma 3 and 8 comma minus 3 comma 3 taking 2 on x axis and 3 on y axis we get this point as 2 comma 3 and naming it as c. Now similarly plotting point 8 comma minus 3 we get 8 on x axis and minus 3 on y axis. So, we get this point as our 8 comma minus 3 and name it as d. Extending this line we see that d will lie on this same line. Therefore, we can see both the lines of equation x plus y is equal to 5 and 2x plus 2y is equal to 10 are same. Therefore, this is our required line and we can see that both the lines a b are inside. Therefore, we can write our solution as solution. This is our required answer. I hope you understood the problem. Bye and have a nice day.