Determine whether (2, 6)
and (−7, 9)
are solutions to the system
x−y<3
9x+y>8
(1 point)
Responses
Both ordered pairs are solutions to the system
Both ordered pairs are solutions to the system
Only (−7, 9)
is a solution to the system.
Only (−7, 9)
is a solution to the system.
Only (2, 6)
is a solution to the system.
Only (2, 6)
is a solution to the system.
Neither of the ordered pairs are solutions to the system.
Neither of the ordered pairs are solutions to the system.
To determine if (2, 6) and (-7, 9) are solutions to the system, we need to substitute the x and y values into the inequalities and check if the inequalities are satisfied.
For the first inequality x - y < 3:
- For (2, 6):
2 - 6 = -4 which is less than 3. The inequality is satisfied.
- For (-7, 9):
-7 - 9 = -16 which is less than 3. The inequality is satisfied.
For the second inequality 9x + y > 8:
- For (2, 6):
9 * 2 + 6 = 18 + 6 = 24 which is greater than 8. The inequality is satisfied.
- For (-7, 9):
9 * -7 + 9 = -63 + 9 = -54 which is not greater than 8. The inequality is not satisfied.
Therefore, only the ordered pair (2, 6) is a solution to the system. The answer is "Only (2, 6) is a solution to the system."