Select all of the ordered pairs that are solutions to the following system of inequalities.
8y≥
–
2x–32
4x–8y>0
Questions
The given system of inequalities is:
1) 8y ≥ -2x - 32
2) 4x - 8y > 0
To find the solutions to this system, we need to check which ordered pairs satisfy both inequalities.
Let's solve the first inequality for y:
y ≥ (-2x - 32) / 8
y ≥ -0.25x - 4
Now let's solve the second inequality for y:
y < 0.5x
Now we can check which ordered pairs satisfy both inequalities:
Let's consider some examples:
1) (0, 0)
y ≥ -0.25*0 - 4 => y ≥ -4
0 < 0.5*0
This point does not satisfy the inequalities.
2) (4, 2)
y ≥ -0.25*4 - 4 => y ≥ -5
2 < 0.5*4
This point satisfies both inequalities.
3) (-6, -3)
y ≥ -0.25*(-6) - 4 => y ≥ -1.5 - 4 => y ≥ -5.5
-3 < 0.5*(-6)
This point satisfies both inequalities.
4) (10, 5)
y ≥ -0.25*10 - 4 => y ≥ -6
5 < 0.5*10
This point satisfies both inequalities.
Therefore, the ordered pairs (4, 2), (-6, -3), and (10, 5) are solutions to the given system of inequalities.