Select all of the ordered pairs that are solutions to the following system of inequalities.
6x≥8–3y
–4x–y≤9
a) 9,0
b) -4,5
c) -1,6
d) 2,3
To determine which ordered pairs are solutions to the system of inequalities, we can plug in the x and y values into both inequalities and see if they are true statements.
a) (9,0)
6(9) ≥ 8 - 3(0)
54 ≥ 8
True
-4(9) - 0 ≤ 9
-36 ≤ 9
True
So, (9,0) is a solution to the system of inequalities.
b) (-4,5)
6(-4) ≥ 8 - 3(5)
-24 ≥ -7
True
-4(-4) - 5 ≤ 9
16 - 5 ≤ 9
True
So, (-4,5) is a solution to the system of inequalities.
c) (-1,6)
6(-1) ≥ 8 - 3(6)
-6 ≥ -10
True
-4(-1) - 6 ≤ 9
4 - 6 ≤ 9
False
So, (-1,6) is not a solution to the system of inequalities.
d) (2,3)
6(2) ≥ 8 - 3(3)
12 ≥ -1
True
-4(2) - 3 ≤ 9
-8 - 3 ≤ 9
True
So, (2,3) is a solution to the system of inequalities.
Therefore, the ordered pairs that are solutions to the system of inequalities are:
a) 9,0
b) -4,5
d) 2,3