X_____ -4z=1 2x-y-6z=4 2x+3y-2z=8 Use substitution method find complete solution?

1 Answers

Oddman Profile
Oddman answered
Add 4z to the first equation to get an expression that will substitute for x.

  x = 1 + 4z Use this in the other two equations.
  2(1+4z) - y - 6z = 4    (substitute into the second equation)
  -y + 2z = 2    (subtract 2, collect terms)  [eqn 4]

  2(1+4z) + 3y - 2z = 8    (substitute into the third equation)
  3y + 6z = 6    (subtract 2, collect terms)  [eqn 5]

We can solve [eqn 5] for y and substitute the result into [eqn 4].

  y + 2z = 2    (divide [eqn 5] by 3)
  y = 2 - 2z    (subtract 2z)  [eqn 6]

  -(2 - 2z) + 2z = 2    (substitute for y in [eqn 4])
  4z = 4    (add 2, collect terms)
  z = 1    (divide by 4)

Put this value of z into [eqn 6] to find y
  y = 2 - 2(1)
  y = 0
Likewise, use the value of z in our expression for x
  x = 1 + 4(1)
  x = 5
The complete solution is x=5, y=0, z=1.

Answer Question

Anonymous