Whakaoti mō a (complex solution)
\left\{\begin{matrix}a=-\frac{by-cz}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&\left(b=\frac{cz}{y}\text{ and }y\neq 0\text{ and }x=0\right)\text{ or }\left(z=0\text{ and }y=0\text{ and }x=0\right)\text{ or }\left(c=0\text{ and }y=0\text{ and }x=0\right)\end{matrix}\right.
Whakaoti mō b (complex solution)
\left\{\begin{matrix}b=-\frac{ax-cz}{y}\text{, }&y\neq 0\\b\in \mathrm{C}\text{, }&\left(a=\frac{cz}{x}\text{ and }x\neq 0\text{ and }y=0\right)\text{ or }\left(z=0\text{ and }y=0\text{ and }x=0\right)\text{ or }\left(c=0\text{ and }y=0\text{ and }x=0\right)\end{matrix}\right.
Whakaoti mō a
\left\{\begin{matrix}a=-\frac{by-cz}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&\left(b=\frac{cz}{y}\text{ and }y\neq 0\text{ and }x=0\right)\text{ or }\left(z=0\text{ and }y=0\text{ and }x=0\right)\text{ or }\left(c=0\text{ and }y=0\text{ and }x=0\right)\end{matrix}\right.
Whakaoti mō b
\left\{\begin{matrix}b=-\frac{ax-cz}{y}\text{, }&y\neq 0\\b\in \mathrm{R}\text{, }&\left(a=\frac{cz}{x}\text{ and }x\neq 0\text{ and }y=0\right)\text{ or }\left(z=0\text{ and }y=0\text{ and }x=0\right)\text{ or }\left(c=0\text{ and }y=0\text{ and }x=0\right)\end{matrix}\right.
Pātaitai
Linear Equation
a x + b y = c z
Tohaina
Kua tāruatia ki te papatopenga
ax=cz-by
Tangohia te by mai i ngā taha e rua.
xa=cz-by
He hanga arowhānui tō te whārite.
\frac{xa}{x}=\frac{cz-by}{x}
Whakawehea ngā taha e rua ki te x.
a=\frac{cz-by}{x}
Mā te whakawehe ki te x ka wetekia te whakareanga ki te x.
by=cz-ax
Tangohia te ax mai i ngā taha e rua.
yb=cz-ax
He hanga arowhānui tō te whārite.
\frac{yb}{y}=\frac{cz-ax}{y}
Whakawehea ngā taha e rua ki te y.
b=\frac{cz-ax}{y}
Mā te whakawehe ki te y ka wetekia te whakareanga ki te y.
ax=cz-by
Tangohia te by mai i ngā taha e rua.
xa=cz-by
He hanga arowhānui tō te whārite.
\frac{xa}{x}=\frac{cz-by}{x}
Whakawehea ngā taha e rua ki te x.
a=\frac{cz-by}{x}
Mā te whakawehe ki te x ka wetekia te whakareanga ki te x.
by=cz-ax
Tangohia te ax mai i ngā taha e rua.
yb=cz-ax
He hanga arowhānui tō te whārite.
\frac{yb}{y}=\frac{cz-ax}{y}
Whakawehea ngā taha e rua ki te y.
b=\frac{cz-ax}{y}
Mā te whakawehe ki te y ka wetekia te whakareanga ki te y.
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