 Hello and welcome to the session. In this session we discussed the following question which says show graphically that the system of equations 2x plus 4y equal to 10, 3x plus 6y equal to 12 is inconsistent. So for the given system of equations we have to show graphically that the system of equations is inconsistent. So first of all for this we should know that what would be the condition for the given system of linear equations to be inconsistent. Consider the system of equations a1x plus b1y plus c1 equal to 0, a2x plus b2y plus c2 equal to 0. Let this be equation 1 and this be equation 2. Let line l1 represent the graph of equation 1 and line l2 represent the graph of equation 2. Now when the two lines l1 and l2 are parallel that is when l1 is parallel to the line l2 then the system of equations have no common solution that is we say the system is inconsistent. So when we are given a system of equations we will draw the graphs of both these equations and see if the lines representing the equations are parallel to each other then the system would be inconsistent. This is the key idea that we use for this question. Now let's proceed with the solution. The given system of equations is 2x plus 4y is equal to 10 and 3x plus 6y is equal to 12. Let this be equation 1 and this be equation 2. Consider the equation 2x plus 4y equal to 10. We take two common on the left hand side so inside the bracket we have x plus 2y is equal to 10. This means x plus 2y is equal to 10 upon 2 that is 5. So we have rewritten equation 1 as x plus 2y equal to 5. So now we will draw the graph of the equation x plus 2y equal to 5. So now we will put some values for x and find the corresponding values of y for the given equation x plus 2y equal to 5. So when we put x equal to 1 let's see what would be the value of y that is obtained from the given equation. So when x is equal to 1 we get 1 plus 2y is equal to 5 that is 2y is equal to 4 which means that y is equal to 2. So for x equal to 1 y is equal to 2. When we take x equal to 3 then we have 3 plus 2y is equal to 5 which means that 2y is equal to 2 from here we get y is equal to 1. So for x equal to 3 y is equal to 1. So thus we have now obtained two points a point a with coordinates 1, 2 and a point b with coordinates 3, 1. Now to obtain the graph of the equation x plus 2y equal to 5 we will plot these two points on the graph. First consider the point a with coordinates 1, 2. Let's plot this point on the graph. Now here the x coordinate is 1 so from the origin we will move one unit to the right. So we reach here. Now as the y coordinate is 2 so from this point we will move two units upwards along the y axis. So we reach at this point this point is the point a with coordinates 1, 2. Now consider the point b with coordinates 3, 1. Let's plot this point now. Now here the x coordinate is 3 so from the origin we move three units to the right along the x axis. We reach at this point. Now as the y coordinate is 1 so from this point we move one unit upwards along the y axis. So we reach at this point. So this point is the point b with coordinates 3, 1. Now we join the points a and b. So this line a b represents the equation 2x plus 4y is equal to 10. That is we can say line a b represents equation 1. Now let's consider the other equation which is 3x plus 6y is equal to 12. Now we take 3 common on the left hand side. Inside the bracket we have x plus 2y is equal to 12. This gives us x plus 2y is equal to 12 upon 3 which is 4. So we have rewritten equation 2 as x plus 2y equal to 4. Now we will draw the graph of this equation. Now here again we will take some values for x and find the corresponding values for y. When we take x equal to 0 then we have 0 plus 2y equal to 4. So this gives us 2y equal to 4 which means y is equal to 4 upon 2 that is 2. So for x equal to 0 y is equal to 2. And when we take x equal to 2 we get 2 plus 2y equal to 4 which means 2y is equal to 4 minus 2 that is 2. And from here we get y is equal to 2 upon 2 equal to 1. So for x equal to 2 y is equal to 1. So thus we have obtained 2 points say a point c which coordinates 0, 2 and a point d which coordinates 2, 1. Now we shall plot these two points on the graph. First consider the point c which coordinates 0, 2. So we will plot this point on the graph. Now here the x coordinate is 0. So we start from the origin and the y coordinate is 2. So we will move 2 units upwards along the y axis. So we reach at this point. So this is the point c which coordinates 0, 2. Now the other point is point d which coordinates 2, 1. Here the x coordinate is 2. So we will move 2 units towards right from the origin. So we reach at this point. And 1 unit upwards along the y axis and see y coordinate is 1. So we get this point. This is the point d which coordinates 2, 1. Now we join the point c and d. So we get this line cd. This line cd represents the equation 3x plus 6y equal to 12. That is the line cd represents the equation 2. Now as you can see the lines a, b and cd are parallel. So this means the given system of equations have no common solution. That is it is inconsistent. So we have shown that the given system of equations is inconsistent. With this we complete the session. Hope you have understood the solution for this question.