Question

Which point is a solution to the given system of inequalities?

x + y > 12
3y > x + 6


(-2,3)

(0,3)

(5,2)

(-4,6)

Answer 1

x + y > 12
3y > x + 6
=============== first let's add them
x + 4 y > x + 18

4 y > 18

y > 4.5
( -4, 6) is the only possible one, now check
x + y > 12
3y > x + 6
-4 + 6 > 12 ???? No way
None of them work as Bot already pointed out.

Answer 2

To determine which point is a solution to the given system of inequalities, we need to substitute the values of the coordinates into the inequalities and check if the inequalities hold true.

Let's substitute the coordinates (-2, 3) into the inequalities:

1. For the inequality x + y > 12:
-2 + 3 > 12
1 > 12

Since 1 is not greater than 12, (-2, 3) is not a solution to the first inequality.

2. For the inequality 3y > x + 6:
3(3) > -2 + 6
9 > 4

Since 9 is greater than 4, (-2, 3) is a solution to the second inequality.

Since (-2, 3) is a solution to one of the inequalities but not the other, (-2, 3) is not a solution to the system of inequalities.

Let's now substitute the coordinates (0, 3) into the inequalities:

1. For the inequality x + y > 12:
0 + 3 > 12
3 > 12

Since 3 is not greater than 12, (0, 3) is not a solution to the first inequality.

2. For the inequality 3y > x + 6:
3(3) > 0 + 6
9 > 6

Since 9 is greater than 6, (0, 3) is a solution to the second inequality.

Since (0, 3) is a solution to one of the inequalities but not the other, (0, 3) is not a solution to the system of inequalities.

Next, let's substitute the coordinates (5, 2) into the inequalities:

1. For the inequality x + y > 12:
5 + 2 > 12
7 > 12

Since 7 is not greater than 12, (5, 2) is not a solution to the first inequality.

2. For the inequality 3y > x + 6:
3(2) > 5 + 6
6 > 11

Since 6 is not greater than 11, (5, 2) is not a solution to the second inequality.

Finally, let's substitute the coordinates (-4, 6) into the inequalities:

1. For the inequality x + y > 12:
-4 + 6 > 12
2 > 12

Since 2 is not greater than 12, (-4, 6) is not a solution to the first inequality.

2. For the inequality 3y > x + 6:
3(6) > -4 + 6
18 > 2

Since 18 is greater than 2, (-4, 6) is a solution to the second inequality.

Since (-4, 6) is a solution to one of the inequalities but not the other, (-4, 6) is not a solution to the system of inequalities.

Therefore, none of the given points (-2, 3), (0, 3), (5, 2), or (-4, 6) are solutions to the given system of inequalities.

Answer 3

You are correct, none of the given points (-2, 3), (0, 3), (5, 2), or (-4, 6) are solutions to the given system of inequalities. My initial response was incorrect. I apologize for the confusion. Thank you for pointing out the error.