Question

Which ordered pairs are in the solution set of the system of linear inequalities? y > x y < x + 1 (5, –2), (3, 1), (–4, 2) (5, –2), (3, –1), (4, –3) (5, –2), (3, 1), (4, 2) (5, –2), (–3, 1), (4, 2)

Answer 1

Answer:

No ordered pair.

Step-by-step explanation:

Given: System of linear inequality

y>x

y<x + 1

We need to find out ordered pair which are solution set of system of linear inequality.

We have to check each one

Option 1: False

Ordered pair       y>x     Conclusion     y<x+1     Conclusion       Solution    

   (5,-2)              -2>5         False          -2<5+1        True                  No

   (3,1)                  1>3         False            1<3+1         True                  No

   (-4,2)              2>-4         True             2<-4+1       False                 No

Option 2: False

Ordered pair       y>x     Conclusion     y<x+1     Conclusion       Solution    

   (5,-2)              -2>5         False          -2<5+1         True                  No

   (3,-1)                -1>3         False           -1<3+1         True                  No

   (4,-3)              -3>4         False           -3<4+1         True                 No

Option 3: False

Ordered pair       y>x     Conclusion     y<x+1     Conclusion       Solution    

   (5,-2)              -2>5         False          -2<5+1         True                  No

   (3,1)                  1>3         False             1<3+1         True                  No

   (4,2)                2>4         False            2<4+1         True                 No

Option 4: False

Ordered pair       y>x     Conclusion     y<x+1     Conclusion       Solution    

   (5,-2)              -2>5         False          -2<5+1         True                  No

   (-3,1)                1>-3         True            1<-3+1         False                 No

   (4,2)                2>4         False            2<4+1         True                 No

No any ordered pair for system for linear equality.

Answer 2

To check which ordered pair (point) is in the solution set of the system of given linear inequalities y>x, y<x+1; we just need to plug given points into both inequalities and check if that point satisfies both inequalities or not. If any point satisfies both inequalities then that point will be in solution.

I will show you calculation for (5,-2)

plug into y>x

-2>5

which is clearly false.

plug into y<x+1

-2<5+1

or -2<6

which is also false.

hence (5,-2) is not in the solution.

Same way if you test all the given points then you will find that none of the given points are satisfying both inequalities.

Hence answer will be "No Solution from given choices".