Which of the following points are a solution to the simultaneous inequalities y ≤ -x + 2 and y > 1x+3?
• (6,7)
• (5,5)
• (-10,-1)
• (4,-6)
To determine which points are solutions to the simultaneous inequalities, we can substitute the x and y values of each point into the inequalities and see if the inequalities hold true.
For point (6,7):
y ≤ -x + 2 gives us 7 ≤ -6 + 2, which is false.
y > 1x + 3 gives us 7 > 1(6) + 3, which is true.
Therefore, (6,7) is a solution to the simultaneous inequalities.
For point (5,5):
y ≤ -x + 2 gives us 5 ≤ -5 + 2, which is true.
y > 1x + 3 gives us 5 > 1(5) + 3, which is true.
Therefore, (5,5) is a solution to the simultaneous inequalities.
For point (-10,-1):
y ≤ -x + 2 gives us -1 ≤ 10 + 2, which is true.
y > 1x + 3 gives us -1 > 1(-10) + 3, which is false.
Therefore, (-10,-1) is not a solution to the simultaneous inequalities.
For point (4,-6):
y ≤ -x + 2 gives us -6 ≤ -4 + 2, which is true.
y > 1x + 3 gives us -6 > 1(4) + 3, which is false.
Therefore, (4,-6) is not a solution to the simultaneous inequalities.
In conclusion, the solutions to the simultaneous inequalities y ≤ -x + 2 and y > 1x + 3 are (6,7) and (5,5).