e (2x +y + 22 =2 13x-y-22= -6 1-3x+y + 10 Z=6
Respuestas a la pregunta
Respuesta:
x = -1/7 , y = -138/7 , z = 85/7
2x +y + 22 = 2. (1)
13x-y-22= -6. (2)
1-3x+y+10z = 6 (3)
Método de Sustitución :
1 ) Despejamos " x " en " 13x-y-22 = -6 " :
13x-y-22 = -6
13x-y-22+22 = -6+22
13x-y = 16
13x-y+y = 16+y
13x = 16+y
13x/13 = (16+y)/13
x = (16+y)/13
2 ) Reemplazamos a " x = (16+y)/13 " en " 2x+y+22 = 2 " :
2((16+y)/13)+y+22 = 2
13((16+y)/13)+13(y)+13(22) = 13(2)
16+y+13y+286 = 26
16+14y+286 = 26
14y+302 = 26
14y/2+302/2 = 26/2
7y+151 = 13
7y+151-151 = 13-151
7y = -138
7y/7 = -138/7
y = -138/7
3 ) Sustituimos " y = -138/7 '' en '' 2x+y+22 = 2 '' :
2x+(-138/7)+22 = 2
2x-138/7+22 = 2
7(2x)-7(138/7)+7(22) = 2(7)
14x - 138+154 = 14
14x +16 = 14
14x/2+16/2 = 14/2
7x + 8 = 7
7x+8-8 = 7-8
7x = -1
7x/7 = -1/7
x = -1/7
4 ) Sustituimos a " x = -1/7 " y a " y = -138/7 " en " 1-3x+y+2z = 6 " :
1-3(-1/7)+(-138/7)+2z = 6
1+3/7-138/7 + 2z = 6
1+(-135/7)+2z = 6
1-135/7 + 2z = 6 , 1 = 7/7
7/7-135/7 +2z = 6
-128/7 + 2z = 6
7(-128/7)+7(2z) = 6(7)
-128+14z = 42
-128+14z+128 = 42+128
14z = 170
14z/2 = 170/2
7z = 85
7z/7 = 85/7
z = 85/7
Explicación paso a paso: