 Hello friends, let's discuss the following question. It says solve the following system of inequalities graphically. Let us move on to the solution. The first inequality given to us is 3x plus 4y is less than equal to 60. And its corresponding equation of line is 3x plus 4y is equal to 60. Now to draw this line we need to have two points. So if y is 0 then x is equal to 20. And if x is 0 then y is equal to 15. So to draw the line 3x plus 4y is equal to 60 we need to plot the ordered pairs 20, 0 and 0, 15. Let us now draw the line 3x plus 4y is equal to 60. For that we need to plot the ordered pairs 20, 0 and 0, 15. So when x is 20 y is 0 that is this point. And when x is 0 y is 15 that is this point. Now we join these two points to get the line 3x plus 4y is equal to 60. Now we have to identify the region for the inequality 3x plus 4y less than equal to 60. For that we take any point not lying on the line 3x plus 4y is equal to 60. 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 in general we take that point to be 0, 0 as it does not lie on the line 3x plus 4y is equal to 60. So when x is 0 y is 0 the inequality becomes 3 into 0 plus 4 into 0 less than equal to 60 that 0 is less than equal to 60 which is true that means 0, 0 satisfies inequality 3x plus 4y less than equal to 60. So we will shade the region which contains the point 0, 0 for the inequality 3x plus 4y less than equal to 60. Now this is the region which contains the point 0, 0 for the inequality 3x plus 4y less than equal to 60. So we shade this region since the inequality contains less than equal to sin we need to darken the line as it shows that the line is included in the solution region. Now the second inequality given to us is x plus 3y less than equal to 30. Now we need to have two points to draw the line x plus 3y is equal to 30. So if y is 0 then x is equal to 30 and if x is 0 then y is equal to 10. So we need to plot the ordered pairs 30, 0 and 0, 10. Let us now draw the line x plus 3y is equal to 30 for that we need to plot the points 30, 0 and 0, 10. Now when x is 30, y is 0 so this is this point and when x is 0, y is 10 so it is this point. Now we join these two points to get the line x plus 3y is equal to 30. Now to identify the region for the inequality x plus 3y less than equal to 30 we take the point 0, 0 as it does not lie on the line x plus 3y is equal to 30 and we will see whether it satisfies this inequality or not. So when x is 0, y is 0 the inequality becomes 0 plus 3 into 0 less than equal to 30. That is 0 is less than equal to 30 which is true. That means 0, 0 satisfies inequality x plus 3y less than equal to 30. So we will shade the region which contains the point 0, 0 for the inequality x plus 3y less than equal to 30. Now this is the region which contains the point 0, 0 for the inequality x plus 3y less than equal to 30. So we shade this region. Now we also need to darken the line x plus 3y is equal to 30 because the inequality contains the sign less than equal to which shows that this line is also included in the solution region. Now we are also given the inequality x greater than equal to 0 and y greater than equal to 0. That means each point in the solution region lies in the first quadrant. Now we see that region in red is common to all the solution regions and this is the required solution region and this completes the question. For now take care, have a good day.