 Hello friends. Let's work out the following problem. It says solve the following system of inequalities graphically. So let's move on to the solution. The first inequality given to us is x plus y greater than 4 and its corresponding equation of line is x plus y is equal to 4. Now to draw this line we need to have two points if we take y as 0 that gives us x as 4 and if we take x as 0 that gives us y as 4. So in order to draw the line x plus y is equal to 4 we need to plot the point 4, 0 and 0, 4. So let's draw the line. These are the coordinate x's and we have to draw the line x plus y is equal to 4 and for that we need to plot the point 4, 0 and 0, 4. Now when x is 4, y is 0. When x is 4, y is 0. So it is this point and when x is 0, y is 4. So it is this point. Now let's join these points to get the line x plus y is equal to 4. We have to shape the region x plus y greater than 4. For that we take any point not lying on the line x plus y is equal to 4 and we check whether that point satisfies this region or not. If that point satisfies this region we will shape the region which contains that point and generally we take that point to be 0, 0. Now we see that 0 plus 0 greater than 4 that is 0 greater than 4 is not true. So the point 0, 0 does not satisfy the region plus y greater than 4. So we will shape the region which does not contain the point 0, 0 for the inequality x plus y greater than 4. So let us shape the region which does not contain the point 0, 0. This is the point 0, 0 and we have to shape the region which does not contain the point 0, 0. So the region would be this because this region does not contain the point 0, 0. Now the second inequality given to us is 2x minus y greater than 0 and its corresponding equation of line is 2x minus y is equal to 0. Now to draw this line we need to have 2 points. So when y is 0 then x is also 0 and when y is equal to 2 then x is equal to 1 and if is equal to 4 then x is equal to 2. So if we want to draw this line we need to plot the points 0, 0, 1, 2 and 2, 4. Now we have to draw the line 2x minus y is equal to 0. For that we need to plot the point 0, 0, 1, 2 and 2, 4. Now 0, 0 is here that means the line will pass through origin. When x is 1 y is 2 it is this point and when x is 2 y is 4 so it is this point. Let us now join these points to get the line 2x minus y is equal to 0. Now we have to shade the region for the inequality 2x minus y greater than 0. For that we take any point not lying on the line 2x minus y is equal to 0 and we will check whether that point satisfies this region or not. If that point satisfies this region we will shade the region containing that point. If that point does not satisfy this region we will shade the region which does not contain that point. Now we take that point to be 1, 1. Now we cannot take that point to be 0, 0 because the 0, 0 lies on the line 2x minus y is equal to 0. So we are taking that point to be 1, 1 as we can see that the point 1, 1 does not lie on the line 2x minus y is equal to 0. Now if we take x is 1 and y is 1 the inequality becomes 2 into 1 minus 1 greater than 0 that is 1 greater than 0 which is true. That means the point 1, 1 satisfies the region x minus y greater than 0. Now for the inequality 2x minus y greater than 0 we will shade the region which contains the point 1, 1. Now this is the line 2x minus y is equal to 0 and we have to shade the region for the inequality 2x minus y greater than 0 which contains 1, 1. Now this is the region which contains 1, 1 so we shade this region. Now we have shaded both the regions and region in red is common to both the regions and it is the solution region for the given system of inequalities. So this completes the question. Hope you enjoyed the session. Goodbye and take care.