Question

ecuasiones lineales
porfa
y=2x+1
2y=x+8

Answer 1

Respuesta:

y = 2x+1

2y = x+8

Método de Reducción :

1 ) Se multiplica la ecuación " 2y = x+8 " por -1/2 :

-1/2(2y = x+8)

-1/2(2y) = -1/2(x+8)

-1/2(2y) = -1/2(x)+(-1/2)(8)

-y = -1/2(x)+(-8/2)

-y = -1/2(x)+(-4)

-y = -1/2(x)-4

2 ) Se suma la ecuación resultante " -y = -1/2(x)-4 " con la ecuación " y = 2x+1 " :

-y = -1/2(x)-4

+

y = 2x+1

-----------------------

(-1+1)y = (-1/2+2)x+(-4+1) ====== > 0 = (-1/2+2)x+(-3) ===== > 0 = (-1/2+2)-3 ==== > 0+3 = (-1/2+2)x-3+3 ====== > 3 = (-1/2+2)x ==== > ( -1/2+2)x = 3 ; 2 = 4/2

==== > (-1/2+(4/2))x = 3 ==== > ((-1+4)/2)x = 3 ======== > (3/2)x = 3

3 ) Se calcula el valor de " x " en la ecuación resultante " (3/2)x = 3 " :

(3/2)x = 3

2(3/2)x = 2(3)

3x = 6

(3/3)x = 6/3

x = 2

4 ) Se reemplaza a " x = 2 " en la ecuación " 2y = x+8 " :

2y = x+8 ; x = 2

2y = (2)+8

2y = 10

(2/2)y = 10/2

y = 5

5 ) Se comprueba :

(5) = 2(2)+1

5 = 4+1

5 = 5

2(5) = (2)+8

10 = 10

R// Por ende , ( x , y ) = ( 2 , 5 ) es el conjunto solución del sistema de ecuaciones lineales dado con anterioridad .