Final answer:
Option D, (1, -4), is the solution to the system of linear inequalities.
Step-by-step explanation:
To determine which of the given points is a solution of the system of linear inequalities, we can substitute the x and y values of each point into the inequalities and check if they satisfy the inequalities.
Let's start with option A, (-1, -1). Substituting these values into the inequalities, we get:
-1 > -(-1) - 5 (Equation 1)
-1 < -(-1) - 3 (Equation 2)
By solving these equations, we find that -1 > -4 and -1 < -2, which means that (-1, -1) is not a solution to the system of inequalities.
We can repeat this process for the remaining options to determine which one is a solution.
After checking all the options, we find that option D, (1, -4), is the only solution to the system of linear inequalities. When we substitute these values into the inequalities, we get:
-4 > -(1) - 5 (Equation 3)
-4 < -(1) - 3 (Equation 4)
By solving these equations, we find that -4 > -6 and -4 < -2, which means that (1, -4) is the solution to the system of inequalities.