Solving the system of equations with the substitution method, we have:
- x - y - z = -8 Equation (1)
- 4x + 4y + 5z = 7 Equation (2)
2x + 2z = 4 Equation (3)
2x=4 - 2z (Subtracting 2z from both sides of the equation 3)
x=2- z (Dividing by 2 on both sides of equation 3)
-x-z=-8+y (Adding y to both sides of equation 1)
-x-z+8=y (Adding 8 to both sides of the equation 1)
Replacing the previous results in the equation 2, we have:
-4(2-z) + 4(-(2-z)-z+8)+ 5z = 7
-8+4z+4(-2+z-z+8)+5z = 7 (Distributing)
-8+4z+4(-2+8)+5z=7 (Subtracting like terms)
-8+4z-8+32+5z=7 (Distributing)
9z+16=7 (Adding like terms)
9z=-9 (Subtracting 16 from both sides of the equation)
z=-1( Dividing by 9 on both sides of the equation)
Replacing z in the equation x=2-z
x=2-(-1)=2+1=3
Replacing x=3 and z=-1 in the equation -x-z+8=y
-3-(-1)+8=y
-3+1+8=y
6=y
The answers are:
x=3
y=6
z=-1