Mathematics, 25.08.2019 14:50 jonathan3191

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

Answers: 2

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Answers

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

Answer from: brevancci

-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 from: Quest

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Answer from: Quest

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

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