multi-variable equations

Use the matrix/determinant function MDETERM() to solve simultaneous equations:
1. You must write the equations in STANDARD FORM, i.e.,

X1+ Y1 + Z1 = C1

X2+ Y2 + Z2 = C2

X3+ Y3 + Z3 = C3

Put each numeric value in a cell, for your example, using cells A1:D3 the matrix is:

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Copy/paste cells A1:C3 three times, these will be your X, Y & Z determinants.
Next, copy cells D1:D3
Paste these D values over the:
X column of the X determinant,
Y col of the Y det'mt, &
Z col of the Z det'mt, thus:

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Use the function: MDETERM() to calculate four determinants:
The first determinant using =MDETERM(A1:C3) is the determinant D of the matrix and will be the divisor.

Use the MDETERM fn on each of the remaining three arrays and divide the results of each by D

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Therefore:
X = 255/-4.5 = -56.67
Y = -476/-4.5 = 105.78
Z= -86/-4.5 = 19.11