The point that satisfies both inequalities is B. (-3, -1).
To find which point satisfies the system of inequalities y>x−2 and y>2x+2, you can test each point given in the options by substituting the x and y values into the inequalities.
Let's test the points one by one:
A. (1, -6)
For x=1 and y=−6:
y>x−2 becomes −6>1−2 which is false.
y>2x+2 becomes −6>2(1)+2 which is false.
So, (1, -6) does not satisfy both inequalities.
B. (-3, -1)
For x=−3 and y=−1:
y>x−2 becomes −1>−3−2 which is true.
y>2x+2 becomes
−1>2(−3)+2 which is true.
So, (-3, -1) satisfies both inequalities.
C. (-1, -6)
For x=−1 and y=−6:
y>x−2 becomes −6>−1−2 which is false.
y>2x+2 becomes
−6>2(−1)+2 which is false.
So, (-1, -6) does not satisfy both inequalities.
D. (3, -1)
for x=3 and y=−1:
y>x−2 becomes −1>3−2 which is false.
y>2x+2 becomes −1>2(3)+2 which is false.
So, (3, -1) does not satisfy both inequalities.
Therefore, the point that satisfies both inequalities is B. (-3, -1).
Question
The graph below represents the following system of inequalities
y > x - 2
y > 2x + 2
Which point (x,y) satisfies the given system of inequalities
A. (1,-6)
B. (-3,-1)
C. (-1,-6)
D. (3,-1)