# Math (linear algebra)

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Solve the system of equation.

x- 2y+ 3z = 5
3x + y = -5
-2x+y + z = 8

• Math (linear algebra) -

x- 2y+ 3z = 5
3x + y = -5
-2x+y + z = 8

First thing to check is that we have three equations and three unknowns, which is fine. If there are more unknowns than equations then there is a problem with the question.

x- 2y+ 3z = 5
3x + y = -5
-2x+y + z = 8

we need to eliminate one unknown by combining pairs of equations. Lets say we remove the y terms.

x- 2y+ 3z = 5
3x + y = -5 (multiply by 2)

x- 2y+ 3z = 5
6x + 2y = -10

Add these two and y terms are removed.

7x+3z=-5

Do the same with, but this time subtract the two and the y terms are removed

3x + y = -5
-2x+y + z = 8

5x-z=-13

We now have two equations and two unknwons

7x+3z=-5
5x-z=-13 (multiply by 3)

7x+3z=-5
15x-3z=-39

22x=-44, so x=-2

substitute in here to find y
3x + y = -5

the substitute in one of the above to find z

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