Question

Solve by elimination
-4x-5y-z=18
-2x-5y-2z=12
-2x+5y+2z=4

Answer 1

-4x - 5y - 1z = 18 ⇒ -4x - 5y - 1z = 18
-2x - 5y - 2z = 12 ⇒ -2x - 5y - 2z = 12
-2x + 5y + 2z = 4 -6x - 10y - 3z = 30
-6(-4) - 10y - 3z = 30
-4x - 5y - 1z = 18 24 - 10y - 3z = 30
-2x - 5y - 2z = 12 ⇒ -2x - 5y - 2z = 12 - 24 - 24
-2x + 5y + 2z = 4 ⇒ -2x + 5y + 2z = 4 -10y - 3z = 6
-4x = 16 -10y + 10y - 3z = 6 + 10y
-4 -4 -3z = 6 + 10y
x = -4 -3 -3
z = -2 - 3¹/₃y
-10y - 3(-2 - 3¹/₃y) = 6
-10y + 6 + 10y = 6
-10y + 10y + 6 = 6
0y + 6 = 6
- 6 - 6
0y = 0
0 0
y = 0
-10(0) - 3z = 6
-0 - 3z = 6
0 - 3z = 6
- 0 - 0
-3z = 6
-3 -3
z = -2
(x, y, z) = (-4, 0, -2)

Answer 2

so

-4x-5y-z=18
-2x-5y-2z=12
-2x+5y+2z=4

the 2 last equations look perfect for canceling each other so add them together

-2x-5y-2z=12
-2x+5y+2z=4 +
-4x+0y+0z=16
-4x=16
divide both sides by 4
-x=4
multiply -1
x=-4

now we have
-4x-5y-z=18
-2x+5y+2z=4
add them together
-6x+0y+z=22
but x=-4 so
-6(-4)+z=22
24+z=22
subtract 24 from both sides
z =-2

subsitute into any equation
-2x-5y-2z=12

x=-4
z=-2
-2(-4)-5y-2(-2)=12
8-5y+4=12
12-5y=12
subtract 12 from both sides
-5y=0
y=0


x=-4
y=0
z=-2