Question

Solve the System. Give your answer as (x, y, z).

-3x + 2y - 4z = 1
-6x-2y - 5z = 8
12x - 2y-z = -10
(x, y, z) =
=
=
=

Answer 1

(x, y, z) = (-1, -1, 0)

Explanation:

You want the solution to the system of equations ...

• -3x +2y -4z = 1
• -6x -2y -5z = 8
• 12x -2y -z = -10

Solution

The calculator solution is shown in the attachment.

(x, y, z) = (-1, -1, 0)

Ad hoc

The coefficient of the y-variable is 2 or -2, which means we can eliminate y terms by adding pairs of equations. Adding the first equation to each of the other two reduces the system to ...

• -9x -9z = 9
• 9x -5z = -9

Adding these two equations together gives ...

-14z = 0 ⇒ z = 0

Substituting this into the second of the reduced equations gives ...

9x = -9 ⇒ x = -1

And substituting for x and z in the first of the original equations gives ...

-3(-1) +2y = 1

2y = -2 . . . . . . . . subtract 3

y = -1

The solution is (x, y, z) = (-1, -1, 0).

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