Answer:
2) x = -4; y = 0; z = -2
4) x = 4; y = 2; z = 0
Step-by-step explanation:
2)
-4x - 5y - z = 18
-2x - 5y - 2z = 12
-2x + 5y + 2z = 4
Add the 2nd and 3rd equations to eliminate y and z.
-4x = 16
x = -4
Substitute x = -4 in first and second equations.
(-4)(-4) - 5y - z = 18
(-2)(-4) - 5y - 2z = 12
-5y - z = 2
-5y - 2z = 4
Multiply first equation by -1 and add to second equation.
5y + z = -2
(+) -5y - 2z = 4
----------------------
-z = 2
z = -2
Substitute x = -4 and z = -2 in first original equation and solve for y.
-4(-4) - 5y - (-2) = 18
16 - 5y + 2 = 18
-5y = 0
y = 0
Answer: x = -4; y = 0; z = -2
4)
4x + 4y + z = 24
2x - 4y + z = 0
5x - 4y - 5z = 12
Add equations 1 and 3 to eliminate y.
9x - 4z = 36 Eq. 1
Add equations 1 and 2 to eliminate y.
6x + 2z = 24 Eq. 2
Multiply Eq. 2 by 2 and add to Eq. 1.
12x + 4z = 48
(+) 9x - 4z = 36
----------------------------
21x = 84
x = 4
Substitute x = 4 into Eq. 1 to solve for z.
9x - 4z = 36
9(4) - 4z = 36
-4z = 0
z = 0
Substitute x = 4 and z = 0 into the first original equation to solve for y.
4x + 4y + z = 24
4(4) + 4y + 0 = 24
4y = 8
y = 2
Answer: x = 4; y = 2; z = 0
