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we conclude that only two points (-5, 5) and (-1, 4) satisfy the system of inequalities.

Step-by-step explanation:

Given the system of inequalities

y > 2x+3

y+3x ≤ 1

Checking the point (0, 5)

Let us substittue the point (0, 5) to check if it is satisfies system of inequalities

y > 2x+3

5 > 2(0) + 3

5 > 3

True

now check for the second inequality

y+3x ≤ 1

5 + 3(0) ≤ 1

5 ≤ 1

False

Therefore, the point (0, 5) does not satisfy the system of inequalities

Checking the point (-5, 5)

Let us substittue the point (-5, 5) to check if it is satisfies system of inequalities

y > 2x+3

5 > 2(-5) + 3

5 > -10+3

5 > -7

True

now check for the second inequality

y+3x ≤ 1

5 + 3(-5) ≤ 1

5-15 ≤ 1

-10 ≤ 1

True

Therefore, the point (-5, 5) satisfies the system of inequalities.

Checking the point (-1, 4)

Let us substittue the point (-1, 4) to check if it is satisfies system of inequalities

y > 2x+3

4 > 2(-1) + 3

4 > -2+3

4 > 1

True

now check for the second inequality

y+3x ≤ 1

4 + 3(-1) ≤ 1

4-3 ≤ 1

1 ≤ 1

True

Therefore, the point (-1, 4) satisfies the system of inequalities.

Checking the point (0, -5)

Let us substitute the point (0, -5) to check if it satisfies the system of inequalities

y > 2x+3

-5 > 2(0) + 3

-5 > 0+3

-5 > 3

False

now check for the second inequality

y+3x ≤ 1

-5 + 3(0) ≤ 1

-5+0 ≤ 1

-5 ≤ 1

True

Therefore, the point (0, -5) does not satisfy the system of inequalities.

Checking the point (-3, -3)

Let us substitute the point (-3, -3) to check if it satisfies the system of inequalities

y > 2x+3

-3 > 2(-3) + 3

-3 > -6+3

-3 > -3

False

now check for the second inequality

y+3x ≤ 1

-3 + 3(-3) ≤ 1

-3 - 9 ≤ 1

-12 ≤ 1

True

Therefore, the point (-3, -3) does not satisfy the system of inequalities.

Hence, we conclude that only two points (-5, 5) and (-1, 4) satisfy the system of inequalities.

step-by-step explanation: