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User Dvdgld
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Answer:

x = -4,

y = 3,

z = 2

Explanation:

{2x - y + z = -9,

{3x + 2y - 4z = -14

{x + z = -2;

First, let's make x the subject from the 3rd equation:

x = -2 - z

Replace x in the 1st and the 2nd equations with its value from the 3rd equation:

{2 * (-2 - z) - y + z = -9,

{3 * (-2 - z) + 2y - 4z = -14;

Now, we have a new system of equations

Let's eliminate the brackets (multiply every term inside the bracket by the term on the outside):

{-4 - 2z - y + z = -9,

{-6 - 3z + 2y - 4z = -14;

Collect like-terms (also, when moving the terms to the other side, make sure to change their signs into the opposite of the previous ones):

{-y - z = -9 + 4,

{2y - 7z = -14 + 6;

.

{-y - z = -5,

{2y - 7z = -8;

Let's make y the subject from the 1st equation:

-y = -5 + z / : (-1)

y = 5 - z

Replace y in the 2nd equation with its value from the 1st one:

2 × (5 - z) - 7z = -8

Expand the brackets:

10 - 2z - 7z = -8

Collect like-terms:

-9z = -8 - 10

-9z = -18 / : (-9)

z = 2

y = 5 - 2 = 3

x = -2 - 2 = -4

User Matt Becker
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