Answer:
Question 1: True
Question 2: True
Question 3: False
Question 4: True
Question 5 True
Explanation:
You have to replace the variables 'x' and 'y' by the given value inside the pair of each question and see if the inequalities are verified or not.
Question 1:
Pair is (3,-2), so x = 3 and y = -2
If you enter these in the provided inequalities, do they verify them (once you changed the values of x and y, is the inequality true or not)?
We'll verify the first inequality...
y ≤ x - 3 becomes -2 ≤ 3 - 3 becomes -2 ≤ 0
We replaced the variables x and y by the values given in the question, and made the calculations to simplify the expression.
Now, is -2 smaller or equal to 0? yes.
Let's verify the second inequality of question 1
y ≥ -x -2 becomes -2 ≥ -(3) -2 becomes -2 ≥ -5
Is -2 greater or equal to -5? Yes.
Since both inequalities are verified (are true), the answer to the question 1 is TRUE.
Question 2
Pair is (1,4), so x = 1 and y = 4
We'll verify the first inequality...
y > -3x + 3 becomes 4 > -3(1) + 3 becomes 4 > -3 + 3 becomes 4 > 0
That is true.
We'll verify the second inequality...
y > x + 2 becomes 4 > 1 + 2 becomes 4 > 3
Again this is true.
Since BOTH inequalities are true, the answer to the question 2 is TRUE.
Question 3:
Pair is (0,-2), so x = 0 and y = -2
We'll verify the first inequality...
y ≤ 3x - 6 becomes -2 ≤ 3(0) - 6 becomes -2 ≤-6
Is -2 less or equal to -6? No of course.
Since one is not true, the answer to the question 3 is FALSE.
Question 4:
Pair is (0,3), so x = 0 and y = 3
We'll verify the first inequality...
2x - y < 4 becomes 2(0) - 3 < 4 becomes -3 < 4
That is true.
Let's verify the second one:
x + y > -1 becomes 0 + 3 > -1 becomes 3 > -1
Which is also true. so the answer to the question 4 is TRUE.
Question 5:
Pair is (-3,0), so x = -3 and y = 0
We'll verify the first inequality...
y > 2x - 3 becomes 0 > 2(-3) - 3 becomes 0 > -6 -3 becomes 0 > -9
which is true.
the second one now...
y < -x + 6 becomes 0 < -(-3) + 6 becomes 0 < 9
Which is also true. so the answer to the question 5 is TRUE.