Respuesta :
The values of (x,y,z) are (3,-1,-2) , if the given are equations [tex]2x+2y+z=- 2[/tex],[tex]-x-2y+2z=-5[/tex] and [tex]2x+4y+z=0[/tex].
Step-by-step explanation:
The given is,
[tex]2x+2y+z=- 2[/tex].......................................(1)
[tex]-x-2y+2z=-5[/tex]......................................(2)
[tex]2x+4y+z=0[/tex].........................................(3)
Step:1
Equation (2) is multiplied by -1 ( Eqn(2) × -1 )
[tex]x+2y-2z=5[/tex].............................(4)
Subtract the equation (1) and (4)
[tex]2x+2y+z=- 2[/tex]
[tex]x+2y-2z=5[/tex]
( - )
[tex](2x-x)+(2y-2y)+(z+2z)=(-2-5)[/tex]
[tex]x+3z=-7[/tex]......................(5)
Step:2
Equation (2) is multiplied by -2 ( Eqn(2) × -2)
[tex]2x+4y-4z=10[/tex]........................(6)
Subtract equation (6) and (3),
[tex]2x+4y-4z=10[/tex]
[tex]2x+4y+z=0[/tex]
( - )
[tex](2x-2x)+(4y-4y)+(-4z-z)= (10-0)[/tex]
[tex]-5z=10[/tex]
[tex]z = - \frac{10}{5}[/tex]
z = -2
From the equation (5),
[tex]x+3z=-7[/tex]
[tex]x+(3)(-2)=-7[/tex]
[tex]x = -7+6[/tex]
x = -1
From equation (1),
[tex]2x+2y+z=- 2[/tex]
Substitute x and z values,
[tex](2)(-1)+2y+(-2)=-2[/tex]
[tex]2y - 4=2[/tex]
[tex]2y=4-2[/tex]
[tex]2y=2[/tex]
[tex]y=\frac{2}{2}[/tex]
y = 1
Step:3
Check for solution,
[tex]-x-2y+2z=-5[/tex]
Substitute x,y and z values,
[tex]-(-1)-(2)(1)+(2)(-2)=-5[/tex]
[tex]1-2-4=-5[/tex]
-5 = -5
Result:
The values of (x,y,z) are (3,-1,-2) , if the given are equations [tex]2x+2y+z=- 2[/tex],[tex]-x-2y+2z=-5[/tex] and [tex]2x+4y+z=0[/tex].
