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Solve for (x,y,z)
x + 5y + 5z = -10
x + y +z= 2
x + 2y + 3z = -3​

User Jeffpowrs
by
8.2k points

1 Answer

1 vote

Answer:

  • (5, -1, -2)

Explanation:

Given system:

  • x + 5y + 5z = -10
  • x + y + z = 2
  • x + 2y + 3z = -3​

Eliminate one of the variables.

Subtract the second equation from the first and from the third equation:

  • x + 5y + 5z - x - y - z = -10 - 2 ⇒ 4y + 4z = -12 ⇒ y + z = -3
  • x + 2y + 3z - x - y - z = -3 - 2 ⇒ y + 2z = -5

Now subtract the first equation above from the second to solve for z:

  • y + 2z - y - z = -5 + 3
  • z = -2

Find y:

  • y + z = -3
  • y - 2 = -3
  • y = 2 - 3
  • y = -1

Now find x:

  • x + y + z = 2
  • x - 1 - 2 = 2
  • x - 3 = 2
  • x = 2 + 3
  • x = 5

The solution is:

  • (5, -1, -2)
User Yuriy Mayorov
by
8.5k points

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