9x+y is less than or equal to 1700
9x+3y is less than or equal to 1800
4x+8y is less than or equal to 2400
***I need help plugging in numbers for x and y. The numbers don't have to be the same for each question.
To find numbers that satisfy the given inequalities, we can solve the system of linear inequalities simultaneously by graphing.
Step 1: Solve each inequality for y in terms of x:
1) 9x + y ≤ 1700
y ≤ 1700 - 9x
2) 9x + 3y ≤ 1800
3y ≤ 1800 - 9x
y ≤ (1800 - 9x) / 3
y ≤ 600 - 3x
3) 4x + 8y ≤ 2400
8y ≤ 2400 - 4x
y ≤ (2400 - 4x) / 8
y ≤ 300 - 0.5x
Step 2: Now, let's graph these inequalities on a coordinate plane:
1) Graph the line y = 1700 - 9x. Since it's an inequality, draw the line as a dashed line. Choose any two values for x and find the corresponding y-values.
2) Graph the line y = 600 - 3x in the same manner as the previous step.
3) Graph the line y = 300 - 0.5x.
Step 3: Shade the region below each line to satisfy the inequalities. Since we need to find the values that make all three inequalities true, the desired region is the intersection of the shaded regions.
The common shaded region is the solution to the problem. You can now pick any points within the overlapping shaded region to get the desired values for x and y.