 Hello and welcome to the session. Let's discuss the following question. It says solve the following system of inequalities graphically. So let us move on to the solution. The first inequality given to us is 3x plus 2y less than equal to 150 and its corresponding equation of line is 3x plus 2y is equal to 150. Now to draw this line we need to have two points. So if y is 0 then x is equal to 50 and if x is 0 then y is equal to 75. So we need to plot the ordered pairs 50 0 and 0 75 to draw the line 3x plus 2y is equal to 150. So we have drawn the line 3x plus 2y is equal to 150 by plotting the points 50 0 and 0 75. Now we have to identify the region for the inequality 3x plus 2y less than equal to 50. For that we take any point not lying on the line 3x plus 2y is equal to 50 and we check whether that point satisfies this inequality 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. Now we take that point to be 0 0 as it does not lie on the line 3x plus 2y is equal to 150. So the inequality becomes 3 into 0 plus 2 into 0 is less than equal to 150 that is 0 is less than equal to 150 which is true. That means 0.00 satisfies the inequality 3x plus 2y less than equal to 150. So we will shape the region which contains the point 0 0 for the inequality 3x plus 2y less than equal to 150. Now this is the region which contains the point 0 0 for the inequality 3x plus 2y less than equal to 150. So we shape this region. This is the solution region for the inequality 3x plus 2y less than equal to 150 and this solution region also includes the line 3x plus 2y is equal to 150. So we darken this line. Now the second inequality given to us is x plus 4y less than equal to 80 and its corresponding equation of line is x plus 4y is equal to 80. Now if y is 0 then x is equal to 80 and if x is 0 then y is equal to 20. So we need to plot the ordered pairs 80 0 and 0 20. To draw the line x plus 4y is equal to 80. So let's now draw the line x plus 4y is equal to 80. For that we need to plot the ordered pairs 80 0 and 0 20. When x is 80 y is 0 so it is this point and when x is 0 y is 20 so it is this point. Now we join these two points to get the required line. Now we have to identify the region for the inequality x plus 4y less than equal to 80 and we see that 0 0 satisfies the inequality x plus 4y less than equal to 80 as 0 plus 4 into 0 is less than 80 that is 0 is less than 80. So we will shade the region which contains the point 0 0 for the inequality x plus 4y less than equal to 80. Now this is the region which contains the point 0 0 let us below the line x plus 4y is equal to 80 which contains the point 0 0 so we shade this region so this is the solution region for the inequality x plus 4y less than equal to 80 and the solution region also includes the line x plus 4y is equal to 80. So we make it dark and this is the solution region for the inequality x plus 4y less than equal to 80. Now the third inequality given to us is x less than equal to 15 and its corresponding equation of line is x is equal to 15. Now we draw the line x is equal to 15 here is x is equal to 15 so we draw this line now we have to shade the region for the inequality x less than equal to 15. Now here we have 15 x is equal to 15 so this is the region which we have to shade that means x less than equal to 15. So we now shade this region for the inequality x less than equal to 15 and it also includes the line x is equal to 15 because the inequality contains the less than equal to sign. So we make a dark line now we are also given y is greater than equal to 0 that means the region above x axis because we know that x axis is a line y is equal to 0 that means y greater than equal to 0 is the region above x axis and including x axis. Now we see that the region in brown is common to all the four regions and it is the required solution region. So this completes the question bye for now take care have a good day.