 Hi and welcome to the session. Let's discuss the following question. It says solve the following system of inequalities graphically. So let's move on to the solution. The first inequality given to us is 2x minus y greater than 1 and its corresponding equation of line is 2x minus y is equal to 1. Now to draw this line we need to have two points. So if we take y as 0 that gives us x is equal to 1 by 2 and if we take x as 0 that gives us y is equal to minus 1. So in order to draw the line 2x minus y is equal to 1 we need to plot the points 1 by 2, 0 and 0 minus 1. Let's now draw the line 2x minus y is equal to 1. These are the coordinate axis and we have to draw the line 2x minus y is equal to 1 and for that we need to plot the points 1 by 2, 0 and 0 minus 1. Now when x is 1 by 2 y is 0 so the point is here and when x is 0 y is minus 1 so the point is this. Let's now join these two points to get the line 2x minus y is equal to 1. So this is the line 2x minus y is equal to 1. Now we have to sheet the region for the inequality 2x minus y greater than 1. For that we take any point not like on the line 2x minus y is equal to 1 and we'll decide whether that point satisfies this region or not. If that point satisfies this region we'll sheet the region containing that point and if that point doesn't satisfy this region we'll sheet the region which doesn't contain that point. So in general we take that point to be 0, 0. Now if x is 0 and y is 0 then the inequality becomes 2 into 0 minus 0 greater than 1 that is 0 greater than 1 which is not true that means the point 0, 0 does not satisfy the region x minus y greater than 1. So we'll sheet the region for the inequality 2x minus y greater than 1 which does not contain 0, 0. Now we have to sheet the region for the inequality 2x minus y greater than 1 which does not contain 0, 0. Here is 0, 0. So we have to sheet the region which does not contain 0, 0. So this would be the region. So let's sheet this region. This is the solution region for first inequality. Now the second inequality given to us is x minus 2y is less than minus 1 and it's corresponding equation of line is x minus 2y is equal to 1 and to draw this line we need to have two points. So when y is 0 that gives us x is equal to minus 1 and if x is 0 that gives us y as 1 upon 2. So in order to draw this line we need to plot the points minus 1, 0 and 0, 1 upon 2. Now we have to draw the line x minus 2y is equal to minus 1. For that we need to plot the points minus 1, 0 and 0, 1 by 2. So let's plot the points. If x is minus 1 then y is 0 say it is this point and if x is 0 then y is 1 upon 2. Let's now join these two points to get the line x minus 2y is equal to minus 1. Now we have to sheet the region for the inequality x minus 2y less than minus 1. So we take any point not lying on the line x minus 2y is equal to minus 1. So let's take that point to be 0, 0 and if x is 0, y is 0 then the inequality becomes 0 minus 2 into 0 less than minus 1 that is 0 is less than minus 1 which is not true because 0 is greater than minus 1 that means the point 0, 0 does not satisfy the region x minus 2y less than minus 1. So we will shade the region for the inequality x minus 2y less than minus 1 which does not contain 0, 0. This is the line x minus 2y is equal to minus 1 and we have to shade the region which does not contain 0, 0. So it should be this region. So let's now shade this region. We have shaded the region for the inequality x minus 2y less than minus 1 and the region in red is common to both the regions and it is the solution region that is the region in red is the solution region for the given system of inequalities 1 and 2. So this completes the question. Hope you enjoyed this session. Goodbye and take care.