Answers:
(4, 3)
(6, 0)
(3, -1)
Step-by-step explanation:
An ordered pair is a solution to the system of inequalities if when we replace x and y, the ordered pair satisfies both equations.
So, for (4, 3), we get:
y ≤ 5x - 4
3 ≤ 5(4) - 4
3 ≤ 20 - 4
3 ≤ 16
y ≥ -2x - 1
3 ≥ -2(4) - 1
3 ≥ -8 - 1
3 ≥ -9
Therefore, (4, 3) is a solution of the system since 3 is less than 16 and 3 is greater than -9.
For (6, 0), we get:
y ≤ 5x - 4
0 ≤ 5(6) - 4
0 ≤ 30 - 4
0 ≤ 26
y ≥ -2x - 1
0 ≥ -2(6) - 1
0 ≥ -12 - 1
0 ≥ -13
Therefore, (6, 0) is a solution of the system
For (-4, -3), we get:
y ≤ 5x - 4
-3 ≤ 5(-4) - 4
-3 ≤ -20 - 4
-3 ≤ -24
Since -3 is greater than -24, (-4, -3) is not a solution to the system.
For (1, 3), we get:
y ≤ 5x - 4
3 ≤ 5(1) - 4
3 ≤ 5 - 4
3 ≤ 1
Since 3 is greater than 1, (1, 3) is not a solution to the system.
Finally, for (3, -1), we get:
y ≤ 5x - 4
-1 ≤ 5(3) - 4
-1 ≤ 15 - 4
-1 ≤ 11
y ≥ -2x - 1
-1 ≥ -2(3) - 1
-1 ≥ - 6 - 1
-1 ≥ -7
Therefore, (3, -1) is a solution to the system.