Which ordered pair does not satisfy the system 2x + y > 0 and -2x - y > -8?

Question

(3, -2)

(2, 3)

(-1, 4)

(-1, -1)

Answer 1

You could save a little work by observing that you can take the second equation -2x - y > -8 and express it equivalently as 2x + y < 8. Then you have 2x + y < 0 and 2x + y < 8 or 0 < 2x + y < 8. So 2x + y must be between 2 and 8 (not inclusive). Then you only need to perform one calculation per ordered pair.

Answer 2

To satisfy the System of Equations means that: if given two equations[2x + y > 0 ; -2x - y > -8], a set of values(Ordered Pair) will make it so that BOTH equations are true.  So, you must plug each set of values, given as  (x , y) into both the equations, and according to the question, only ONE set of the 4 given sets will make it so that the one or both of the equations are NOT true.

You have to plug in each set of values one at a time to figure out which one does NOT satisfy it;

         Here is an example of plugging in one set of values(3 , -2).

             (3 , -2) so, x = 3 ; y = -2

             Now take the first equation[2x + y > 0] and plug in x = 3 ; y = -2

            (2)*(3) + (-2) > 0

           6 - 2 > 0 

           4 > 0 This statement is true.  Now plug x = 3 ; y = -2 into the second equation[-2x - y > -8]

           (-2)*(3) - (-2) > -8

           -6 + 2 > -8

           -4 > -8  This statement is also true.  Therefore, since both equations are true with the plugged in values, we can say that the set of values(3 , -2) satisfies the system of equations, 2x + y > 0 and -2x - y > -8.

          So, we continue on to the next set of values, and the next after that if they satisfy the system of equations.

          ANSWER: The ordered pair (-1 , -1) does NOT satisfy the system of equations, as given by the following:

          (x , y) = (-1 , -1)

          (2)*(-1) + (-1) > 0 :  -2 - 1 > 0

          -3 > 0 is UNTRUE, and thus, fails to satisfy equation one of the system; if it fails to satisfy one of the two equations, then it fails to satisfy the system of equations.

          

Answer 3

Ricky,

  Substitute the x,y pairs into the expressions!

                     2x + y > 0?                 -2x - y > -8?             Both satisfied??

(3, -2)            6 -2 = 4 & >0                 -6 +2 = -4 & >-8               yes

(2, 3)             4 +3 = 7 & >0                -4 -3 = -7 & >-8               yes

(-1, 4)           -2 +4 = 2 & >0                 2 -4= -2 & >-8                 yes

(-1, -1)          -2 -1= -3 & <0             2 +1 = 3 & >-8                 NO

(-1,-1) does not satisfy the conditions together.

Good Luck!

BruceS