Which of the following points are solutions to the system of inequalities shown below?
Check all that apply.
y>4x + 2
y<4x + 5
A. (4, 21)
B. (5, 24)
C. (5, 26)
D. (-4, 20)
5,24
Which coordinates represents a points in the solutions of tje systems of
To determine which of the given points are solutions to the system of inequalities, we need to substitute the x and y values of each point into the inequalities and check if they satisfy the given conditions.
Let's start with point A: (4, 21)
Substituting the x and y values into the inequalities:
For y > 4x + 2, we have 21 > 4(4) + 2, which simplifies to 21 > 16 + 2, and further simplifies to 21 > 18. This is true.
For y < 4x + 5, we have 21 < 4(4) + 5, which simplifies to 21 < 16 + 5, and further simplifies to 21 < 21. This is not true.
Since point A does not satisfy both inequalities simultaneously, it is not a solution to the system of inequalities.
Now let's move on to point B: (5, 24)
Substituting the x and y values into the inequalities:
For y > 4x + 2, we have 24 > 4(5) + 2, which simplifies to 24 > 20 + 2, and further simplifies to 24 > 22. This is true.
For y < 4x + 5, we have 24 < 4(5) + 5, which simplifies to 24 < 20 + 5, and further simplifies to 24 < 25. This is true.
Since point B satisfies both inequalities simultaneously, it is a solution to the system of inequalities.
Moving on to point C: (5, 26)
Substituting the x and y values into the inequalities:
For y > 4x + 2, we have 26 > 4(5) + 2, which simplifies to 26 > 20 + 2, and further simplifies to 26 > 22. This is true.
For y < 4x + 5, we have 26 < 4(5) + 5, which simplifies to 26 < 20 + 5, and further simplifies to 26 < 25. This is not true.
Since point C does not satisfy both inequalities simultaneously, it is not a solution to the system of inequalities.
Lastly, let's consider point D: (-4, 20)
Substituting the x and y values into the inequalities:
For y > 4x + 2, we have 20 > 4(-4) + 2, which simplifies to 20 > -16 + 2, and further simplifies to 20 > -14. This is true.
For y < 4x + 5, we have 20 < 4(-4) + 5, which simplifies to 20 < -16 + 5, and further simplifies to 20 < -11. This is not true.
Since point D does not satisfy both inequalities simultaneously, it is not a solution to the system of inequalities.
To summarize, the only point that is a solution to the system of inequalities is B.
well, did you try actually checking the possibilities?
21 > 16+2 yes
21 < 16+5 no
and so on for the others