Question

Tell whether the ordered pair (10, 5) is a solution of the system of linear inequalities.

y < 2x + 5
y^2 - 4x - 1
a) (10, 5) is a solution.
b) (10, 5) is not a solution.
c) Insufficient information to determine.
d) (10, 5) is a solution for one of the inequalities.

Answer 1

To determine whether the ordered pair (10, 5) is a solution of the system of linear inequalities, we substitute the values of x and y into each inequality and check if both inequalities are true. The ordered pair (10, 5) satisfies one inequality and does not satisfy the other.

Step-by-step explanation:

To determine whether the ordered pair (10, 5) is a solution of the system of linear inequalities, we substitute the values of x and y into each inequality and check if both inequalities are true.

1. For the first inequality y < 2x + 5:

   5 < 2(10) + 5

   5 < 20 + 5

   5 < 25

   This is true, so the ordered pair (10, 5) satisfies the first inequality.

2. For the second inequality y^2 - 4x - 1:

   5^2 - 4(10) - 1

   25 - 40 - 1

   24 - 41

   -17

   This is not true, so the ordered pair (10, 5) does not satisfy the second inequality.

Since the ordered pair (10, 5) satisfies one inequality and does not satisfy the other, the answer is d) (10, 5) is a solution for one of the inequalities.