Question

solve the system by substitution
-x-y-z=-8,
-4x+4y+5z=7,
2x+2z=4

Answer 1

from the 3rd equation :
2x+2z=4, divided by 2 we get :
x+z=2 or
z = 2 - x

now subtitute z = 2 - x into the 1st equation :
-x-y-z=-8
-x-y-(2-x)=-8
-x-y-2+x=-8
-y-2 = -8
-y = -8 + 2
-y = -6
y = 6

subtitute y = 6 into the 1st equation :
-x-y-z=-8
-x-6-z=-8
-x-z=-8+6
-x-z=-2
-x = -2 + z
x = z - 2

again subtitute y = 6 and x = z - 2 into the 2nd equation :
-4x+4y+5z=7
-4(z - 2) + 4(6) + 5z = 7
-4z + 8 + 24 + 5z = 7
z + 32 = 7
z = 7 - 32
z = -25

because x = z - 2 (we got z = -25)
so, x = -25 - 2 = -27

so, the solution (x,y,z) = (-27,6,-25)

Answer 2

looks i make mistake :)
wait a second

Answer 3

given 3 systems :
-x-y-z=-8 ... (1)
-4x+4y+5z=7 ... (2)
2x+2z=4 ... (3)

from the 3rd equation :
2x+2z=4, divided by 2 we get :
x+z=2 or
z = 2 - x ... (let it is the 4th equation)

now subtitute z = 2 - x into the 1st equation :
-x-y-z=-8
-x-y-(2-x)=-8
-x-y-2+x=-8
cancel the x's, it can be
-y-2 = -8 or
-y = -8 + 2
-y = -6
y = 6

then subtitute y = 6 and z = 2 - x into the 2nd equation :
-4x+4y+5z=7
-4x + 4(6) + 5(2 - x) = 7
-4x + 24 + 10 - 5x = 7
-9x + 34 = 7
-9x = 7 - 34
-9x = -27
x = -27/-9
x = 3

finally, subtitute x = 3 into the 4th equation :
z = 2 - x
z = 2 - 3
z = -1

so, the solution (x,y,z) = (3, 6, -1)

Answer 4

thanks you so much ::))))))

Answer 5

you're welcome dear :*