 Hello and welcome to the session. Let us discuss the following question. It says solve the following system of inequalities graphically. The first inequality given to us is 5x plus 4y less than equal to 20, x greater than equal to 1 and the third one is y greater than equal to 2. Let us now move on to the solution. The first inequality given to us is 5x plus 4y less than equal to 20. Now its corresponding equation of line is 5x plus 4y is equal to 20 and to draw this line we need to have 2 points so if x is 0 this implies y is equal to 5 and if y is equal to 0 this implies x is equal to 4. So we need to plot the ordered pairs 0 5 and 4 0 to draw the line 5x plus 4y is equal to 20. So let us now draw the line 5x plus 4y is equal to 20. So let us plot the ordered pairs 0 5 and 4 0 to draw the line 5x plus 4y is equal to 20. That is if x is 0 then y is 5 and if y is 0 then x is 4. Let us now join these points to get the line 5x plus 4y is equal to 20. Now we have to identify the region for the inequality 5x plus 4y less than equal to 20. For that we take any point not lying on the line 5x plus 4y is equal to 20 and we will check whether that point satisfies this inequality or not. If that point satisfies this inequality we will shade the region which contains that point and if that point does not satisfy this inequality we will shade the region which does not contain that point and we take that point to be 0 0. So if x is 0 y is 0 then inequality becomes 5 into 0 plus 4 into 0 less than equal to 20 that is 0 is less than equal to 20 which is true that means the point 0 0 satisfies the inequality 5x plus 4y less than equal to 20. So we will shade the region which contains the point 0 0 for the inequality 5x plus 4y less than equal to 20. Now this is the region which contains the point 0 0 for the inequality 5x plus 4y less than equal to 20. So we shade this region. This is the solution region for the inequality 5x plus 4y less than equal to 20 and the solution region also includes the line 5x plus 4y less than equal to 0. It is the line 5x plus 4y is equal to 20. 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 its corresponding equation of line is x is equal to 1. So let us draw the line x is equal to 1. This is the line x is equal to 1. Now to identify the region for the inequality x greater than equal to 1 we take the point 0 0 and 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 will shade the region which does not contain the point 0 0 for the inequality x greater than equal to 1. So we have to 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 for the inequality x greater than equal to 1. This is the solution region for the inequality x greater than equal to 1 and And the solution region also includes the line x is equal to 1 because the inequality contains the sign greater than equal to, so we darken this line. 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 draw the line y is equal to 2, here we have y is equal to 2, so we draw the line y is equal to 2 here, now again we see that the 0.00 does not satisfy inequality y greater than equal to 2 because if y is 0.00 is greater than equal to 2 which is not true, so we shade the region which does not contain the 0.00 for the inequality y greater than equal to 2, so this is the region above the line which contains which does not contain the 0.00 for the inequality y greater than equal to 2, so we shade this region, so this is the region, this is the solution region for the inequality y greater than equal to 2 and the solution region also includes the line y is equal to 2, so we darken this line. Now we see that the triangular region in black is common to all the three solution regions and this is the required solution region, the triangular region in black and this completes the question, bye for now take care have a good day.