 Hello friends, let's solve the following question. It says solve the following system of inequalities graphically. Let's now move on to the solution. The first inequality given to us is x-2y less than equal to 3. And its corresponding equation of line is x-2y is equal to 3. Now to draw this line we need to have two points. So if y is 0 then x is equal to 3 and if x is equal to 0 then y is equal to minus 3y2. So we need to plot the ordered pairs 3-0 and 0 minus 3y2 to draw the line x-2y is equal to 3. Let's now draw the line x-2y is equal to 3. For that we need to plot the points 3-0 and 0 minus 3y2. When x is 3 y is 0 so it is this point and when x is 0 y is minus 3y2 minus 3y2 means minus 1.5 which is here. Now we join these two points to get the required line. Now we have to identify the region for the inequality x-2y less than equal to 3. For that we take any point not lying on the line x-2y is equal to 3 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. And in general we take that point to be 0-0 and if x is 0 y is 0 the inequality becomes 0 minus 2 into 0 less than equal to 3 that is 0 less than equal to 3 which is true. That means the point 0-0 satisfies inequality x minus 2y less than equal to 3. So we will shape the region which contains the point 0-0 for the inequality x minus 2y less than equal to 3. Now this is the region which contains the point 0-0 for the inequality x minus 2y less than equal to 3. So we shape this region this is the solution region for the first inequality but in the solution region the line is also included because the inequality contains less than equal to sign. So we back in this line to show that this line is included in the solution region. Now the second inequality given to us is 3x plus 4y greater than equal to 12 and its corresponding equation of line is 3x plus 4y is equal to 12. 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 equal to 0 then y is equal to 3. So we need to plot the points 4-0 and 0-3. So let's now draw the line 3x plus 4y is equal to 12 and for that we need to plot the points 4-0 and 0-3. Now when x is 4 y is 0 so it is this point and when x is 0 y is 3 so it is this point. Now we join these two points to get the required line. Now we have to identify the region for this inequality. So we take the point 0-0 as it does not lie on the line 3x plus 4y is equal to 12 and we see that the point 0-0 does not satisfy the inequality 3x plus 4y greater than equal to 12. So we will shape the region which does not contain 0-0 for the inequality 3x plus 4y greater than equal to 12. Now this is the region which does not contain the point 0-0 for the inequality 3x plus 4y greater than equal to 12 so we shape this region. Solution region for the inequality 3x plus 4y greater than equal to 12 and this solution region also includes this line 3x plus 4y is equal to 12 so we make a dark line. Now the third inequality is x greater than equal to 0 and its corresponding equation of line is x is equal to 0. And we know that y-axis is the line x is equal to 0 and we have to shape the region for the inequality x greater than equal to 0. And we know that to the right side of the y-axis all the x are greater than 0 so we shape this region. Solution region for the inequality x greater than equal to 0 and this also includes the line x is equal to 0 because the inequality contains the greater than equal to sign which shows that this line is also included in the solution region. So we darken this line. Now the fourth inequality given to us is y greater than equal to 1 and its corresponding equation of line is y is equal to 1. Now this is y-axis and here y is equal to 1. This is the line y is equal to 1 and we have to shape the region for the inequality y greater than equal to 1. Now above the line y is equal to 1 we have region y greater than equal to 1 so we shape the region above the line y is equal to 1. See that this is the region which is common to all the three regions so we shape this region with another color is common to all the three regions and this is the solution region for the three inequalities and this solution region also contains the line y is equal to 1 because the inequality contains greater than equal to sign. This is the question. Bye for now. Take care. Have a good day.