Question

x+6y=27 en determinantes
7x-3y=9 en determinantes

Answer 1

Respuesta:

7x-3y=9

 

7(27-6y)-3y=9

189-42y-3y=9

-45y=-180

y=4

 

x=27-6*4

x=27-24

x=3

Explicación:

Ecuaciones por Determinantes

Este es el metodo por determinantes Por Ejemplo:  

x+y=-2 <-- Termino Constante T.C.= Termino Constante

-x+4y=17 <-- Termino Constante

Delta=

1 1----------------->1(4) - (-1)(1) ----------------- Delta = 5

-1 4----------------->4+1 = 5

x y

Delta x=

-2 1 --------------> -2(4) - 17(1) ----------------------- Delta = -25

17 4 --------------> -8-17 = -25

T.C. Y

Delta y=

1 -2 ---------------------> 1(17) - (-1)(-2) ---------------------- Delta = 15

-1 17 ---------------------> 17-2 = 15

x T.C.

Delta x= Delta x / Delta = -25/5 = -5

Delta y= Delta y / Delta = 15/5 = 3  

(-5, 3)

1) 24x - 12y= -24

3x + 2y= -17

Delta=

24 -12 ------------------> 24(2)- 3(-12) ---------------- Delta=84

3 2 ------------------> 48-(-36)

-------------------------> 48+36=84

Delta x=

-24 -12 --------------------> -24(2)- (-17)(-12)---------- Delta=-252

-17 2 ---------------------> -48 - 204= -252

Delta y=

24 -24---------------------> 24(-17) - 3 (-24) ----------------------- Delta= -336

3 -17---------------------> -408 - (-72)

--------------------> -408+72= -336  

Delta x= Delta x/Delta = -252/84 = -3

Delta y= Delta y/Delta = -336/84 = -4

(-3,-4)

2) x+6y=27

7x-3y=9

Delta=

1 6------------------------->1(-3) - 7(6) ---------------------------- Delta= -45

7 -3-------------------------> -3 - 42= -45

Delta x=

27 6----------------------> 27(-3) - 9(6) ---------------------- Delta x= -135

9 -3----------------------> -81 -54= -135

Delta y=

1 27 -------------------------> 1 (9) - 7 (27) -------------- Delta= -180

7 -3 -------------------------> 9 - 189= -180

Delta x= Delta x/Delta= -135/-45= 3

Delta y= Deltay/Delta= -180/-45= 4

(3,4)

3) 9x - 4y= 5

7x + 8y= 13

Delta=

9 -4----------------------> 9(8) - 7 (-4) ---------------------- Delta= 100

7 8----------------------> 78 - (-28)

----------------------> 78 + 28= 100

Delta x=

5 -4----------------------> 5(8) - 13(-4) ------------------ Delta=92

13 8----------------------> 40 - (-52)

----------------------> 40 + 52= 92

Delta y=

9 5 ----------------------> 9(13) - 7(5) --------- Delta=82

7 13----------------------> 117 - 35=82

Delta x= Delta x/Delta = 92/100= 0.9

Delta y= Delta y/Delta = 82/100=0.8