Question

Question 1 (1 point)

(05.06)
Which of the following points lie in the solution set to the following system of inequalities? (1 point)

y < −3x + 3
y < x + 2

a
(1, −5)

b
(1, 5)

c
(5, 1)

d
(−1, 5)

HELP PLEASE

Answer 1

The point (1, -5) satisfies both inequalities y < -3x + 3 and y < x + 2, making it the correct option that lies within the solution set of the system.

Step-by-step explanation:

To determine which point lies in the solution set of the system of inequalities y < -3x + 3 and y < x + 2, we need to test each option to see if it satisfies both inequalities.

• For point (1, -5):
  • Substituting x = 1 and y = -5 into the first inequality: -5 < -3(1) + 3, which simplifies to -5 < 0. This is true.
  • Substituting into the second inequality: -5 < 1 + 2, which simplifies to -5 < 3. This is also true.
• Therefore, point (1, -5) satisfies both inequalities and lies within the solution set.

We do not need to test the other points, as only one option can be correct and we have already found the solution.