Question

Solve the system by elimination (show all work)

-2x +2y+3z=0,


-2x-y+z=-3,


2x+3y+3z=5

Answer 1

`[1, 1, 0]`

Explanation:

{−2x + 2y + 3z = 0

{−2x - y + z = −3 ←

{2x + 3y + 3z = 5 ←

2y + 4z = 2 ↷

{−2x + 2y + 3z = 0 ←

{−2x - y + z = −3

{2x + 3y + 3z = 5 ←

5y + 6z = 5 ↷

{5y + 6z = 5

{2y + 4z = 2

−⅖[5y + 6z = 5]

{−2y - 2⅖z = −2 >> New Temporary Equation

{2y + 4z = 2

____________

1⅗z = 0

___ _

1⅗ 1⅗

`z = 0` [Plug this back into both equations above to get the y-term of 1, then plugging both z-term and y-term into all three equations at the very top, will give you the x-term of 1];
`1 = y`;
`1 = x`

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