Answer:
(-2, 2)
Step-by-step explanation:
You can graph the equations and points and see which points fall into the doubly-shaded area. The only one that does is (-2, 2).
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You can also evaluate the inequalities at the given points to see which might work. The inequality y > x is the simplest to evaluate, and it immediately eliminates the last two choices:
-3 > -1 . . . not true
-1 > 0 . . . not true
So, we can check the first two choices in the first inequality:
-(-3) +1 > 5 . . . not true
-(-2) +1 > 2 . . . TRUE
The ordered pair (-2, 2) makes both inequalities true.
Answer:
2nd Option is correct.
Step-by-step explanation:
Given Inequalities are,
y < x + 1 .....................(1)
y > x .....................(2)
To find: Ordered pair which makes he inequalities true.
Pair 1:
x = -3 , y = 5
Inequality (1),
LHS = 5
RHS = -(-3) + 1 = 4
⇒ LHS > RHS
Thus, this pair does not satisfy the pair of inequalities.
Pair 2:
x = -2 , y = 2
Inequality (1),
LHS = 2
RHS = -(-2) + 1 = 3
⇒ LHS < RHS
Inequality (2),
LHS = 2
RHS = -2
⇒ LHS > RHS
Thus, this pair satisfies the pair of inequalities.
Pair 3:
x = -1 , y = -3
Inequality (1),
LHS = -3
RHS = -(-1) + 1 = 0
⇒ LHS < RHS
Inequality (2),
LHS = -3
RHS = -1
⇒ LHS < RHS
Thus, this pair does not satisfy the pair of inequalities.
Pair 4:
x = 0 , y = -1
Inequality (1),
LHS = -1
RHS = -(0) + 1 = 1
⇒ LHS < RHS
Inequality (2),
LHS = -1
RHS = 0
⇒ LHS < RHS
Thus, this pair does not satisfy the pair of inequalities.
Therefore, 2nd Option is correct.
