To solve a set of linear equations in 3 variables, you need 3 equations. As far as I can tell, you have 2 equations here, so the best you can do is write expressions for 2 of the variables in terms of the third.
If you have
x +z +5z = -3y -3
3x -y = -4
Then you can rewrite as
x = -1.5 -0.6z
y = -0.5 -1.8z
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You can get this by any of the usual methods of solving linear equations. Just treat the system as two equations in x and y with the z terms on the right side of the equal sign:
x +3y = -3 -6z
3x -y = -4
