Question

Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.
y>−12x+4y> -\frac{1}{2}x+4
y>−
2

1
​

x+4
y<52x−2y< \frac{5}{2}x-2
y<
2

5
​

x−2

Answer 1

Given :   y >  -x/2   + 4  ,  y <  5x/2   - 2

To find  : coordinates of a point in the solution set.

Solution:

y >  -x/2   + 4

y <  5x/2   - 2

x y > -x/2 + 4 y < 5x/2 - 2

4 6                      8

5 6.5                      10.5

6 7                      13

7 7.5                      15.5

8 8                      18

9 8.5                      20.5

10 9                      23

(4 , 7)

(5 , 7) , ( 5 , 8) , ( 5 , 9) , ( 5 , 10)

(6 , 8) , (6 , 9) , (6 , 10) , (6 , 11 )  (6 , 12)

(7 , 8) , ( 7 , 9 )  , (7 , 10) , (7 ,11 ) , ( 7 , 12) , (7 , 13) , ( 7 , 14) , ( 7 , 15)

and so on are

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