Anew coffee shop can hold no more than 50 seats the owner wants at least 20 of the seats to be stools and the remaining seats to be recliner if x is the number of stools and y is the number of recliners which graph represents the solution to the system of inequalities x+y 50 x 20

The graph is shown below.

Step-by-step explanation:

Given:

Total seats can be at most 50.

Number of stools are at least 20.

If 'x' represent number of stools and 'y' represent number of recliners, then as per question:

In order to plot the above inequalities, we first plot the lines:

For plotting the line , we find its x and y intercepts.

x intercept:

. So, (50, 0) is a point on the line.

y-intercept:

. So, (0, 50) is a point on the line.

Draw a line passing through these two points. Now, as the inequality is less than or equal to 50, the region below the line (including the line) is the solution region of the line.

Now, the next equation is . This is of the form . Therefore, it is a line parallel to the y-axis and passes through the point (20, 0). As the inequality is greater than or equal to 20, the region to the right of the line (including the line) is the solution region.

Also, the values of 'x' and 'y' can't be negative as they represent number of stools and recliners. So, the solution region below the x and y axis is not included. Only the region that is in the first quadrant is included.

Now, the region common to both the region is the solution of the given system of inequalities. The region is shown in the given graph.

side side side

side angle angle

angle side angle

side angle side

step-by-step explanation: