 Hello friends, let's work out the following problem. It says solve the following system of inequalities graphically. So let's move on to the solution. The first inequality given to us is 2x plus y greater than equal to 8 and its corresponding equation of line is 2x plus y is equal to 8. Now to draw this line we need to have two points. So if y is 0 then x is equal to 4 and if x is 0 then y is equal to 8. So we need to plot the points 4, 0 and 0, 8 to draw the line 2x plus y is equal to 8. Let's now draw the line 2x plus y is equal to 8 and for that we need to plot the points 4, 0 and 0, 8. Now when x is 4, y is 0 so it is this point and when x is 0, y is 8 so it is this point. Now we join these two points to get the line 2x plus y is equal to 8. Now to identify the region for the inequality 2x plus y greater than equal to 8 we take any point not lying on the line 2x plus y is equal to 8 and we'll check whether that point satisfies this inequality or not. If that point satisfies this inequality we'll shape the region which contains that point and if that point doesn't satisfy this inequality we'll shape the region which doesn't contain that point. Now we take that point to be 0, 0 so if x is 0, y is 0 then inequality becomes 2 into 0 plus 0 is greater than equal to 8 that is 0 is greater than equal to 8 which is not true. Hence the point 0, 0 does not satisfy inequality or the region 2x plus y greater than equal to 8 so we'll shape the region for this inequality does not contain 0, 0. Now this is the region which does not contain 0, 0 so let's shape this region inequality 2x plus y greater than equal to 8 contain the sign greater than equal to so we need to darken this line which shows that this line is included in the solution region. Now the second inequality given to us is x plus 2y greater than equal to 10 and its corresponding equation of line is x plus 2y is equal to 10. Now if x is equal to 0 then y is equal to 5 and if y is equal to 0 then x is equal to 10 so in order to draw the line x plus 2y is equal to 10 we need to plot the points 0, 5 and 10, 0 so let's now draw the line x plus 2y is equal to 10 for that we need to plot the points 0, 5 and 10, 0, y is 5 so it is this point and if y is 0 then x is 10 so it is this point now we join these two points to get the line x plus 2y is equal to 10 now we have to identify the region for the inequality x plus 2y greater than equal to 10 so we take the point 0, 0 not lying on the line x plus 2y is equal to 10 now we see that if x is 0 then and y is 0 then the inequality becomes 0 plus 2 into 0 greater than equal to 10 that is 0 is greater than equal to 10 which is not true the point 0, 0 does not satisfy inequality x plus 2y greater than equal to 10 so we will shape the region for the inequality x plus 2y greater than equal to 10 which does not contain 0, 0 so this is the line x plus 2y is equal to 10 and now we will shape the region for the inequality x plus 2y greater than equal to 10 which does not contain 0, 0 so it would be this region so let us now shape this region inequality x plus 2y greater than equal to 10 contains the sign greater than equal to we need to darken this line which shows that this line is included in the solution region of the inequality x plus 2y greater than equal to 10 so we have shaded the regions representing both the inequalities 1 and 2 and the region in red is common to both the solution regions and the solution region is the region in red and it is the required solution region so this completes the question I will now take care have a great day