Answer:
we conclude that only two points (-5, 5) and (-1, 4) satisfy the system of inequalities.
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
- As both equalities are NOT TRUE.
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
- As both inequalities hold 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
- As both inequalities hold 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
- As both equalities are NOT 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
- As both equalities are NOT 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.