 Hello 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 x plus y less than equal to 9 and its corresponding equation of line is x plus y is equal to 9. And to draw this line we need to have two points. So if y is 0 then x is equal to 9 and if x is 0 then y is equal to 9. So we need to plot the points 9 0 and 0 9 to draw the line x plus y is equal to 9. Let's now draw the line x plus y is equal to 9. Now when x is 0 y is 9. So it is this point and when y is 0 x is 9 so it is this point. Now we join these two points to get the required line. Now we have to shape the region representing the inequality x plus y less than equal to 9. For that we take any point not line on the line x plus y is equal to 9 and we'll check whether that point satisfies this inequality or not. If that point satisfies this inequality we'll shape the region which contains that point and if that point doesn't satisfy this inequality we'll shape the region which doesn't contain that point. And we take that point as 0 0. So if x is 0 and y is 0 then the inequality becomes 0 plus 0 is less than equal to 9 which is true. That is 0 is less than equal to 9 is true. That means the point 0 0 satisfies the inequality x plus y less than 9. So for the inequality x plus y less than equal to 9 we'll shape the region which contains the point 0 0. Now this is the line x plus y is equal to 9. Now we shape the region which contains the point 0 0 for the inequality x plus y less than equal to 9. So this is the region which contains the point 0 0 here is 0. So let's now shape this region. Now since the inequality contains the sign less than equal to we darken this line which shows that this line is included in the solution region. Now the second inequality given to us is y greater than x. And the corresponding equation of line is y is equal to x. So if x is 0 then y is 0. If x is 1 then y is 1. So let's now draw the line y is equal to x. y is equal to x is the line passing through the origin and where y is equal to x. So it is this line if x is 1 then y is 1. If x is 0 then y is 0. So it is this line. Now we have to identify the region for the inequality y greater than x. For that we take any point not lying on the line y is equal to x. This is the line y is equal to x and we have to take any point not lying on this line. Now we see that the point 1 2 does not lie on the line y is equal to x. So we take the point as 1 2 and we will check if this point satisfies this inequality we will shape the region which contains this point. Now if x is 1 y is 2 then the inequality is 2 greater than 1 which is true that means the point 1 2 satisfies the inequality y greater than x. So we will shape the region for the inequality y greater than x which contains the point 1 2 to shape the region for the inequality y greater than x which contains the point 1 2 this is the point 1 2 and we have to shape the region which contains this point. So this is the region which contains this point so we will shape this region. So we have shaded the region for the inequality y greater than x and in this the line y is equal to x is not included because the inequality does not contain the sign of equality. Now the third inequality given to us is x greater than equal to 0 and corresponding equation of line is x is equal to 0. Now we know that the y axis is the line x is equal to 0. So this is the line y axis is the line x is equal to 0. Now we know that to the right side of y axis all the x are greater than 0 and to the left side of y axis all the x are less than 0. So we shape the region to the right side of y axis because we have to shape the region for the inequality x greater than equal to 0. So it would be this region now since the inequality contains the sign greater than equal to we need to map in the line x is equal to 0 which shows that the line x is equal to 0 is included in the solution region. Now the region in black is common to all the three regions as it is the required solution region for the system of inequalities 1, 2 and 3. So this completes the question. Bye for now take care have a good day.