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3.7: Resolución de sistemas de desigualdades con dos variables

 

Ejercicio ( PageIndex {2} )

 

Determine si el punto dado es o no una solución al sistema dado de desigualdades.

 

1. ((- 2,1) );

 

( left { begin {array} {l} {y> 3 x + 5} \ {y leq – x + 1} end {array} right. )

 

2. ((- 1, -3) );

 

( left { begin {array} {l} {y geq 3 x – 1} \ {y <- 2 x} end {array} right. )

 

3. ((- 2, -1) );

 

( left { begin {array} {l} {x – 2 y> – 1} \ {3 x – y <- 3} end {array} right. )

 

4. ((0, -5) );

 

( left { begin {array} {c} {5 x – y geq 5} \ {3 x + 2 y <- 1} end {array} right. ) [19459002 ]  

5. ((- frac {1} {2}, 0) );

 

( left { begin {array} {l} {- 8 x + 5 y geq 3} \ {2 x – 3 y <0} end {array} right. ) [ 19459002]  

6. ((- 1, frac {1} {2}) );

 

( left { begin {array} {l} {2 x – 9 y <- 1} \ {3 x - 6 y> – 2} end {array} right. ) [ 19459002]  

7. ((- 1, -2) );

 

( left { begin {array} {c} {2 x – y geq – 1} \ {x – 3 y <6} \ {2 x - 3 y> – 1} end {array} right. )

 

8. ((- 5,2) );

 

( left { begin {array} {c} {- x + 5 y> 10} \ {2 x + y <1} \ {x + 3 y <- 2} end { matriz} right. )

 

9. ((0,3) );

 

( left { begin {array} {l} {y + 4 geq 0} \ { frac {1} {2} x + frac {1} {3} y leq 1 } \ {- 3 x + 2 y leq 6} end {array} right. )

 

10. ((1,1) );

 

( left { begin {array} {l} {y leq – frac {3} {4} x + 2} \ {y geq – 5 x + 2} \ {y geq frac {1} {3} x – 1} end {array} right. )

 

11. ((- 1,2) );

 

( left { begin {array} {l} {y geq x ^ {2} + 1} \ {y <- 2 x + 3} end {array} right. )

 

12. ((4,5) );

 

( left { begin {array} {l} {y <(x - 1) ^ {2} - 1} \ {y> frac {1} {2} x – 1} end {array} right. )

 

13. ((- 2, -3) );

 

( left { begin {array} {l} {y <0} \ {y geq - | x | + 4} end {array} right. )

 

14. ((1,2) );

 

( left { begin {array} {l} {y <| x - 3 | + 2} \ {y geq 2} end {array} right. )

 

15. ( left (- frac {1} {2}, – 5 right) );

 

( left { begin {array} {l} {y leq – 3 x – 5} \ {y> (x – 1) ^ {2} – 10} end {array} derecha. )

 

16. ((- 4,1) )

 

( left { begin {array} {l} {x geq – 5} \ {y <(x + 3) ^ {2} - 2} end {array} right. )

 

17. ( left (- frac {3} {2}, frac {1} {3} right) );

 

( left { begin {array} {l} {x – 2 y leq 4} \ {y leq | 3 x – 1 | + 2} end {array} right. )

 

18, ( left (- 3, – frac {3} {4} right) );

 

( left { begin {array} {l} {3 x – 4 y <24} \ {y <(x + 2) ^ {2} - 1} end {array} right . )

 

19. ((4,2) );

 

( left { begin {array} {l} {y <(x - 3) ^ {2} + 1} \ {y <- frac {3} {4} x + 5} end {array} right. )

 

20. (( frac {5} {2}, 1) )

 

( left { begin {array} {l} {y geq – 1} \ {y <- (x - 2) ^ {2} + 3} end {array} right. )

 
     
Respuesta
     
     

1. Sí

     

3. Sí

     

5. Sí

     

7. Sí

     

9. Sí

     

11. Sí

     

13. No

     

15. Sí

     

17. Sí

     

19. No

     
 
 
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