Algoge Judge

Editorial for Jednačine

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Author: mihailot

Jednačine su: $\frac{A_1}{B_1}*x_1+C_1=D_1$ ~ \frac{A_1}{B_1}*x_1+C_1=D_1~ i $\frac{A_2}{B_2}*x_2+C_2=D_2$ ~\frac{A_2}{B_2}*x_2+C_2=D_2~
Ako u obe jednačine prebacimo $C$ ~C~ na levu stranu i pomnožimo sa $B$ ~B~ dobijamo: $A_1*x_1=(D_1-C_1)*B_1$ ~A_1*x_1=(D_1-C_1)*B_1~ i $A_2*x_2=(D_2-C_2)*B_2$ ~A_2*x_2=(D_2-C_2)*B_2~
Prvu jednačinu množimo sa $A_2$ ~A_2~ a drugu sa $A_1$ ~A_1~: $A_1*A_2*x_1=A_2*(D_1-C_1)*B_1$ ~A_1*A_2*x_1=A_2*(D_1-C_1)*B_1~ i $A_1*A_2*x_2=A_1*(D_2-C_2)*B_2$ ~A_1*A_2*x_2=A_1*(D_2-C_2)*B_2~
Kada je $x_1=x_2$ ~x_1=x_2~ leve strane obe jednakosti će biti jednake pa će biti jednake i desne, $A_2*(D_1-C_1)*B_1=A_1*(D_2-C_2)*B_2$ ~A_2*(D_1-C_1)*B_1=A_1*(D_2-C_2)*B_2~
Isto važi i u drgom pravcu, pa je dovoljno proveriti jednakost $A_2*(D_1-C_1)*B_1=A_1*(D_2-C_2)*B_2$ ~A_2*(D_1-C_1)*B_1=A_1*(D_2-C_2)*B_2~

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