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This paper examines necessary and sufficient conditions under which a system of two equations with eight variables and a system of four equations with twelve variables can be transformed into the basic canonical forms represented by nomograms with oriented transparency.

This paper derives the necessary and sufficient conditions such that the system of equations $x_7=f(x_1,x_2,x_3,x_4,x_5,x_6),x_8=g(x_1,x_2,x_3,x_4,x_5,x_6),x_9=h(x_1,x_2,x_3,x_4,x_{11},x_{12}),x_{10}=l(x_1,x_2,x_3,x_4,x_{11},x_{12})$ can be transformed into the form $A_{1,2}+A_{3,4}=A_{7,8}-A_{5,6}=A_{9,10}-A_{11,12}$ $B_{1,2}+B_3=B_{7,8}-B_5=B_{9,10}-B_{11}$. These equations can be constructed with the help of nomograms with oriented transparency.

The paper derives the necessary and sufficient conditions under which the system of equations $x_6=f(x_1,x_2,x_3,x_4,x_5),x_7=g(x_1,x_2,x_3,x_4,x_5)$ can be transformed into the form $A_{6,7}=A_{1,2}+A_{3,4}+A_{3,5},B_{6,7}=B_{1,2}$ which can be constructed by help of nomogram with a transparent with two degrees of freedom.

This paper derives the necessary and sufficient conditions under which the system of equations $x_7=f(x_1,x_2,x_3,x_4,x_5,x_6),x_8=g(x_1,x_2,x_3,x_4,x_5,x_6)$ can be transformed into the form $A_{7,8}=A_{1,2}+A_{3,4}+A_{5,6},B_{7,8}=B_{1,2}+B_3+B_5$; this can be done with the help of nomograph with a oriented transparent.