Question

Which point is not a solution to the system of inequalities y>x−5 and y≤x+3?

a) (4, -1)
b) (3, 0)
c) (0, 0)
d) (2, -2)

Answer 1

Upon evaluating each given point against the two inequalities, y>x−5 and y≤x+3, point (2, -2) is found to not satisfy the second inequality, making it the point that is not a solution to the system.

Step-by-step explanation:

The student's question 'Which point is not a solution to the system of inequalities y>x−5 and y≤x+3?' can be addressed by testing each point.

• For point (4, -1), the inequalities are -1 > 4 - 5 (true) and -1 ≤ 4 + 3 (true), so (4, -1) satisfies both inequalities.
• For point (3, 0), the inequalities are 0 > 3 - 5 (true) and 0 ≤ 3 + 3 (true), so (3, 0) satisfies both inequalities.
• For point (0, 0), the inequalities are 0 > 0 - 5 (true) and 0 ≤ 0 + 3 (true), so (0, 0) satisfies both inequalities.
• For point (2, -2), the inequalities are -2 > 2 - 5 (true) but -2 ≤ 2 + 3 (false), so (2, -2) does not satisfy the second inequality and hence is not a solution.

Therefore, point (2, -2) is not a solution to the system of inequalities.