Solution:

Given inequalities are:

5x + y ≤ 100

x + y ≤ 60

x ≥ 0

y ≥ 0

To solve the given inequalities, we will use the graphical method.

Graphical Method:

Step 1: Convert the given inequalities into equations by replacing the inequality sign with the equality sign.

5x + y = 100

x + y = 60

x = 0

y = 0

Step 2: Plot the graph of each equation on the xy-plane.

For the equation 5x + y = 100, we need to find two points on the line. We can do this by assigning values to x and y and solving for the other variable.

Let x = 0, then y = 100. So, the point (0, 100) lies on the line.

Let y = 0, then 5x = 100, or x = 20. So, the point (20, 0) lies on the line.

Plot these two points and draw the line passing through them.

For the equation x + y = 60, we can use the same method to find two points on the line.

Let x = 0, then y = 60. So, the point (0, 60) lies on the line.

Let y = 0, then x = 60. So, the point (60, 0) lies on the line.

Plot these two points and draw the line passing through them.

The graph of x = 0 is a vertical line passing through the origin.

The graph of y = 0 is a horizontal line passing through the origin.

Step 3: Shade the region that satisfies all the given inequalities.

To do this, we will test a point in each region to see if it satisfies all the given inequalities.

Let's test the point (0, 0).

5x + y ≤ 100 becomes 5(0) + 0 ≤ 100, which is true.

x + y ≤ 60 becomes 0 + 0 ≤ 60, which is true.

x ≥ 0 is already satisfied by the point (0, 0).

y ≥ 0 is also satisfied by the point (0, 0).

So, the point (0, 0) satisfies all the given inequalities.

Therefore, we shade the region below the line 5x + y = 100, below the line x + y = 60, and to the right of the y-axis.

Conclusion:

The shaded region represents the solution to the given system of inequalities. It includes all the points that satisfy all the given inequalities.

(0,0), (20,0), (10,50), & (0,60)