 Hello friends, let's discuss the following question. It says solve the following system of inequalities graphically. The given system of inequalities are x greater than equal to 3 and y greater than equal to 2. Let us now proceed on with the solution. The first inequality given to us is x greater than equal to 3 and its corresponding equation of line is x is equal to 3. So let us now draw the line x is equal to 3. These are the coordinate x's, this is xx's, this is yx's and here we have x is equal to 3. So we draw the line x is equal to 3 which is parallel to yx's. Now we have to identify the region for the inequality greater than x greater than equal to 3. For that we take any point not lying on the line x is equal to 3 and we'll see whether that point satisfies this inequality or not. If that point satisfies this inequality we'll shade the region which contains that point and if that point doesn't satisfy this inequality we'll shade the region which doesn't contain that point and generally we take that point to be 0 0 as we see that the point 0 0 does not lie on the line x is equal to 3. So x is equal to 0 and the inequality becomes 0 greater than equal to 3 which is not true. That means the point 0 0 does not satisfy the inequality x greater than equal to 3. So we'll shade the region which doesn't contain the point 0 0 for the inequality x greater than equal to 3. Now this is the point 0 0 and we have to shade the region which doesn't contain the point 0 0. So this is the region which doesn't contain the point 0 0, so we shade this region. Now the second inequality given to us is y y greater than equal to 2 and its corresponding equation of line is y is equal to 2. So let us now draw the line y is equal to 2. Here we have y is equal to 2. So let us draw the line y is equal to 2. Now again we have to identify the region for the inequality y greater than equal to 2 and we know that the 0.00 does not lie on the line y is equal to 2. So we take the 0.00 and we will see that whether this point satisfies this inequality or not. So here y is equal to 2. So the inequality y is equal to 0. So the inequality becomes 0 greater than equal to 2 which is not true. That means the 0.00 does not satisfy the inequality y greater than equal to 2. That means we need to shade the region which does not contain the 0.00 for the inequality y greater than equal to 2. Now this is the region which does not contain the 0.00. So we need to shade this region for the inequality y greater than equal to 2. So the region in dark grey is the required solution region which is common to both the regions but both the inequalities contains the sign greater than equal to. That is x greater than equal to 3 and y greater than equal to 2. That means the lines x is equal to 3 and y is equal to 2 are also included in the solution region. So we need to darken the line x is equal to 3 and y is equal to 2. So let us darken the lines to show that the lines are included in the solution region for the given inequalities. This is the required solution region for the given inequalities and this completes the question. Bye for now. Take care. Have a good day.