identify which coordinate points (x,y) below are solutions to the following system of linear inequalities (select ALL that apply)
y<2x-3. x-3y<-6
Answers:
0,-3
3,3
15,7
0,5
-3,-12
5,6
11,12
10,7
To identify which coordinate points are solutions to the given system of linear inequalities, we can substitute the values of x and y into each inequality and check if the inequality is true for each given coordinate.
1) Substituting x = 0 and y = -3 into the first inequality:
-3 < 2(0) - 3
-3 < -3
This inequality is not true, so (0, -3) is not a solution.
2) Substituting x = 3 and y = 3 into both inequalities:
3 < 2(3) - 3
3 < 3
This inequality is not true, so (3, 3) is not a solution.
3) Substituting x = 15 and y = 7 into both inequalities:
7 < 2(15) - 3
7 < 27
This inequality is true for the first inequality.
15 - 3(7) < -6
15 - 21 < -6
-6 < -6
This inequality is not true, so (15, 7) is not a solution.
4) Substituting x = 0 and y = 5 into both inequalities:
5 < 2(0) - 3
5 < -3
This inequality is not true, so (0, 5) is not a solution.
5) Substituting x = -3 and y = -12 into both inequalities:
-12 < 2(-3) - 3
-12 < -9
This inequality is true for the first inequality.
-3 - 3(-12) < -6
-3 + 36 < -6
33 < -6
This inequality is not true, so (-3, -12) is not a solution.
6) Substituting x = 5 and y = 6 into both inequalities:
6 < 2(5) - 3
6 < 7
This inequality is true for the first inequality.
5 - 3(6) < -6
5 - 18 < -6
-13 < -6
This inequality is true for the second inequality.
Therefore, (5, 6) is a solution to both inequalities.
7) Substituting x = 11 and y = 12 into both inequalities:
12 < 2(11) - 3
12 < 22
This inequality is true for the first inequality.
11 - 3(12) < -6
11 - 36 < -6
-25 < -6
This inequality is not true, so (11, 12) is not a solution.
8) Substituting x = 10 and y = 7 into both inequalities:
7 < 2(10) - 3
7 < 17
This inequality is true for the first inequality.
10 - 3(7) < -6
10 - 21 < -6
-11 < -6
This inequality is not true, so (10, 7) is not a solution.
Therefore, the coordinate points that are solutions to the given system of linear inequalities are:
(5, 6)