 Hi and welcome to the session. I'm Kanika and I'm going to help you to solve the following question. The question says solve the following inequality graphically in two-dimensional plane. 2x plus y is greater than equal to 6. Before solving this question we should know that a line divides the Cartesian plane into two half planes and the graph of inequality will be one of the half planes and we shall show the solution by shading in the corresponding half plane. We shall follow the following rules to identify the half plane represented by an inequality. Now according to the first rule we have to take any point AB not on the line. Generally we take this point as 00 and then we have to check whether it satisfies the inequality or not. If the point satisfies the inequality then the inequality represents that particular half plane containing the point. If it does not satisfies the inequality then the other half plane represents the solution and according to the second rule if the sign of equality is also there with the inequality then the line is also included in the solution region so we draw a dog right and according to the last rule if we have a pure inequality then the points on the corresponding line are not to be included in the solution region so we draw a dotted line. With the help of these three rules we will solve the question so always remember these three rules. Now with the solution given inequality is 2x plus y is greater than equal to 6. Now the corresponding equation is 2x plus y is equal to 6. Now we will plot the graph of this equation. For plotting the graph we need at least two solutions of this equation so let's first find the two solutions of this equation. Now when x is equal to 0 then y is equal to 6 and when y is equal to 0 then x is equal to 3. So the two solutions of this equation is 0, 6 and 3, 0. Now we will plot these two points on the graph. So let's make a graph now. The first point which we have to plot is 0, 6. This means when fc is 0 then ordinate is 6. So this is the required point 0, 6 and the second point is 3, 0. This means when ordinate is 0 then fc star is 3. This is the point 3, 0. By the second rule we know that if sign of equality is also there with inequality then line is included in the solution region and so we draw a dark line. Now in the given question we are given that 2x plus y is greater than equal to 6. So sign of equality is also there. That means we will now join these two points by a dark line and this line will be included in the solution region. So now join these two points by a dark line. So this line is representing the equation x plus y is equal to 6. This line divides the plane in two half planes that is 1 and 2. Now according to the first rule we know that for identifying the half plane represented by an inequality we have to take any point ab not on line and then we have to take whether it satisfies the inequality or not. If that point satisfies the inequality then the inequality represents that particular half plane containing the point. If it does not satisfy the inequality then the other half plane represents the solution. Now let's take this point as 0 0. Now we will check whether this point satisfies the given inequality or not. Now the given inequality is 2x plus y is greater than 6. Now substitute x as 0 and y as 0. Now by substituting we get 0 greater than 6 which is not true. The half plane not containing 0 0 represents the inequality x plus y greater than 6. Now look at the graph second half plane does not contain the point 0 0 and in the question we have 2x plus y greater than equal to 6. That means the solution region will contain the line also. So let's now shade this region. So this shaded half plane including this line is the required graphical solution. So the shaded half plane second including the line is the required graphical solution. This is our required answer. So this completes the session. Bye and take care.