 Hi and welcome to the session. Let us discuss the following question. It says solve the following system of inequalities graphically. Let us now begin with the solution. The first inequality given to us is 3x plus 2y less than equal to 12. And the corresponding equation of line is 3x plus 2y is equal to 12. Now to draw this line we need to have at least two points. So if x is equal to 0 that implies y is equal to 6 and if y is equal to 0 that implies x is equal to 4. To draw the line 3x plus 2y is equal to 12 we need to plot the ordered pairs 0 6 and 4 0. So let us now draw the line 3x plus 2y is equal to 12. For that we need to plot the ordered pairs 0 6 and 4 0. That is if x is 0 y is 6 that is this point and if y is 0 x is 4. Let us now join these two points to get the line 3x plus 2y is equal to 12. Now we have to identify the region for the inequality 3x plus 2y less than equal to 12. For that we take any point not lying on the line 3x plus 2y is equal to 12 and we will check whether that point satisfies the inequality 3x plus 2y less than equal to 12 or not. If that point satisfies this inequality we will shape the region which contains that point and if that point doesn't satisfy this inequality we will shape the region which doesn't contain that point. And generally we take that point to be 0 0 as this point does not lie on the line 3x plus 2y is equal to 12. So when x is 0 y is 0 the inequality becomes 3 into 0 plus 2 into 0 less than equal to 12 that is 0 less than equal to 12 which is true. That means the point 0 0 satisfies the inequality 3x plus 2y less than equal to 12. So we will shape the region which contains the point 0 0 for the inequality 3x plus 2y less than equal to 12. Now we have to shape the region which contains the point 0 0 for the inequality 3x plus 2y less than equal to 12. Now this is the region which contains the point 0 0 so we need to shape this region. So this is the solution region for the inequality 3x plus 2y less than equal to 12th and this solution region also includes the line 3x plus 2y is equal to 12 because the inequality contains the sign less than equal to that means this line is also included in the solution region. So we darken this line to show that the line is included in the solution region. Now the second inequality given to us is x greater than equal to 1 and it's corresponding equation of line is x is equal to 1, so let's draw the line x is equal to 1. So here we have x is equal to 1, let's draw the line x is equal to 1 which is parallel to yx is, we have to identify the region for the inequality x greater than equal to 1. For that we take any point not lying on the line x is equal to 1, let's take that point to be 0 0, so if x is 0 then the inequality becomes 0 greater than equal to 1 which is not true that means the point 0 0 does not satisfy the inequality x greater than equal to 1. So we need to shade the region which doesn't contain the point 0 0 for the inequality x greater than equal to 1. So we shade the region which does not contain the point 0 0 for the inequality x greater than equal to 1. This is the region which does not contain the point 0 0, so we shade this region. Also we need to darken the line x is equal to 1 because the inequality contains the sign greater than equal to 2 which shows that the line x is equal to 1 is also included in the solution region. Now the third inequality given to us is y greater than equal to 2 and its corresponding equation of line is y is equal to 2. So let's now draw the line y is equal to 2, here we have y is equal to 2. So let's 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 if y is 0 then 0 greater than equal to not true that means 0 0 does not satisfy the inequality y greater than equal to 2, so we shade the region which doesn't contain the point 0 0 for the inequality y greater than equal to 2. So this is the region which does not contain the point 0 0 for the inequality y greater than equal to 2, so we shade this region. We need to darken the line y is equal to 2 because the inequality contains the sign greater than equal to 2 and it shows that the line y is equal to 2 is included in the solution region. Now we see that the triangular region in black is common to all the three regions and this is the required solution region and this completes the question. Bye for now take care have a good day.