SPLTV

Ax + By + Cz = D ………… (i)

Ex + Fy + Gz = H …………(ii)

Px + Qy + Rz = S ………… (iii)

Eliminasi persamaan (i) dan (ii)

Ax + By + Cz = D xG AGx + BGy + CGz = DG

Ex + Fy + Gz = H xC ECx + FCy + GCz = HC -

(AG – EC)x + (BG – FC)y = DG – HC ............ (4)

Eliminasi persamaan (i) dan (iii)

Ax + By + Cz = D xR ARx + BRy + CRz = DR

Px + Qy + Rz = S xC PCx + QCy + RCz = SC -

(AR – PC)x + (BR – QC)y = DR – SC ............... (v)

Eliminasi persamaan (4) dan (5)

(AG – EC)x + (BG – FC)y = DG – HC x(BR-QC)

(AR – PC)x + (BR – QC)y = DR – SC x(BG-FC)

(AG – EC)(BR-QC)x + (BG – FC)(BR-QC)y = (DG – HC)(BR-QC)

(AR – PC)(BG-FC)x + (BR – QC)(BG-FC)y = (DR – SC)(BG-FC) -

[(AG – EC)(BR-QC) – (AR – PC)(BG-FC)]x = (DG – HC)(BR-QC)

x = (DG – HC)(BR-QC) / [(AG – EC)(BR-QC) – (AR – PC)(BG-FC)]

Masukkan nilai x ke persamaan (iv) atau (v)

misalnya ke persamaan (iv)

(AG – EC)x + (BG – FC)y = DG – HC

(AG – EC) (DG – HC)(BR-QC) / [(AG – EC)(BR-QC) – (AR – PC)(BG-FC) + (BG – FC)y = DG-HC

y = (DG – HC)/ (BG – FC) - (AG – EC) (DG – HC)(BR-QC) / [(AG – EC)(BR-QC) – (AR – PC)(BG- FC) ] (BG – FC)

Masukkan nilai x dan y ke salah satu persamaan awal, persamaan (i), (ii),atau (iii)

misalnya ke persamaan (i)

Ax + By + Cz = D

A (DG – HC)(BR-QC) / [(AG – EC)(BR-QC) – (AR – PC)(BG-FC)] + B (DG – HC)/ (BG – FC) - (AG – EC) (DG – HC)(BR-QC) / [(AG - EC) (BR-QC) – (AR – PC)(BG-FC) ] (BG – FC) + Cz = D

z = D/C - [A (DG – HC)(BR-QC) / [(AG – EC)(BR-QC) – (AR – PC)(BG-FC)] + B ((DG – HC) / (BG – FC)) - (AG – EC) (DG – HC)(BR-QC) / [(AG - EC) (BR-QC) – (AR – PC)(BG-FC) ] (BG – FC)] /C

Jadi,

x = (DG – HC)(BR-QC) / [(AG – EC)(BR-QC) – (AR – PC)(BG-FC)]

y = (DG – HC)/ (BG – FC) - (AG – EC) (DG – HC)(BR-QC) / [(AG – EC)(BR-QC) – (AR – PC)(BG-FC) ] (BG – FC)

z = D/C - [A (DG – HC)(BR-QC) / [(AG – EC)(BR-QC) – (AR – PC)(BG-FC)] + B ((DG – HC) / (BG – FC)) - (AG – EC) (DG – HC)(BR-QC) / [(AG - EC) (BR-QC) – (AR – PC)(BG-FC) ] (BG – FC)] /C