Question

Which of the following is the solution to the following system of inequalities?

( begin cases x + 2y ≤ 54 3x - y ≤ 22 end cases )

a) ( (10, 22) )
b) ( (15, 10) )
c) ( (20, 15) )
d) ( (25, 5) )

Answer 1

The solution to the system of inequalities can be found by substituting the given options into the two inequalities to see which one satisfies both conditions.

Step-by-step explanation:

We are looking to find the solution for a system of inequalities:

1. x + 2y ≤ 54
2. 3x - y ≤ 22

To determine which option is a solution to the system, we need to substitute the x and y values from each option into both inequalities:

• For option a (10,22): Substitute x = 10 and y = 22 into both inequalities. If both inequalities are satisfied, it is the solution.
• For option b (15,10): Substitute x = 15 and y = 10 into both inequalities. If both inequalities are satisfied, it is the solution.
• For option c (20,15): Substitute x = 20 and y = 15 into both inequalities. If both inequalities are satisfied, it is the solution.
• For option d (25,5): Substitute x = 25 and y = 5 into both inequalities. If both inequalities are satisfied, it is the solution.

By carrying out these substitutions, we can determine which option, if any, is a solution to the system of inequalities.