Select all of the ordered pairs that are solutions to the following system of inequalities.
–10x<7y+3
5y>–2x+8
-1,8
8,1
-8,1
8,-1
To find the solutions to the system of inequalities, we need to substitute the x and y values from each ordered pair into the inequalities and see if they are valid.
1. (-1, 8):
-10(-1) < 7(8) + 3
10 < 59
This inequality is true for the first equation.
5(8) > -2(-1) + 8
40 > 10
This inequality is true for the second equation.
Therefore, (-1, 8) is a solution to the system.
2. (8, 1):
-10(8) < 7(1) + 3
-80 < 10
This inequality is true for the first equation.
5(1) > -2(8) + 8
5 > -16
This inequality is true for the second equation.
Therefore, (8, 1) is a solution to the system.
3. (-8, 1):
-10(-8) < 7(1) + 3
80 < 10
This inequality is false for the first equation.
5(1) > -2(-8) + 8
5 > 16
This inequality is false for the second equation.
Therefore, (-8, 1) is not a solution to the system.
4. (8, -1):
-10(8) < 7(-1) + 3
-80 < 4
This inequality is false for the first equation.
5(-1) > -2(8) + 8
-5 > -16
This inequality is false for the second equation.
Therefore, (8, -1) is not a solution to the system.
The solutions to the system of inequalities are (-1, 8) and (8, 1).