Question

Determine the relationship between the point (1, –5) and the given system of inequalities.

y ≤ 3x + 2

y > –2x – 3

Answer 1

Sample Answer: Algebraically, the point (1, -5) satisfies the first inequality, but it does not satisfy the second inequality because -5 is not greater than -5. Graphically, the point (1, -5) lies in the shaded area of the first inequality but lies on the dashed line of the second inequality, which is not inclusive. Therefore (1, -5) is not a solution to the given system of inequalities.

Explanation:

Right on edge 2021

Answer 2

The point does not lie in the solution sets of the given system of inequalities

Explanation:

We need to check whether the point (1,-5) is a solution to the system of inequality

`y\le 3x+2`

`y\:>\:3x+2`

We substitute x=1 and y=-5 into the top inequality:

`-5\le 3*1+2`

`-5\le 3+2`

`-5\le 5`. This is true

We substitute x=1 and y=-5 into the bottom inequality:

`-5\:>\:-2*1-3`

`-5\:>\:-2-3`

`-5\:>\:-5`. This is false.

Since the point does not satisfy both inequalities, it is not a solution to the system of inequalities.