Whakaoti i te Ax+By=C

$$A x + B y = C$$

Whakaoti mō A (complex solution)

$$\left\{\begin{matrix}A=-\frac{By-C}{x}\text{, }&x\neq 0\\A\in \mathrm{C}\text{, }&C=By\text{ and }x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te By mai i ngā taha e rua.

$$Ax=C-By$$

He hanga arowhānui tō te whārite.

$$xA=C-By$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xA}{x}=\frac{C-By}{x}$$

Mā te whakawehe ki te x ka wetekia te whakareanga ki te x.

$$A=\frac{C-By}{x}$$

Whakaoti mō B (complex solution)

$$\left\{\begin{matrix}B=-\frac{Ax-C}{y}\text{, }&y\neq 0\\B\in \mathrm{C}\text{, }&C=Ax\text{ and }y=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te Ax mai i ngā taha e rua.

$$By=C-Ax$$

He hanga arowhānui tō te whārite.

$$yB=C-Ax$$

Whakawehea ngā taha e rua ki te y.

$$\frac{yB}{y}=\frac{C-Ax}{y}$$

Mā te whakawehe ki te y ka wetekia te whakareanga ki te y.

$$B=\frac{C-Ax}{y}$$

Whakaoti mō A

$$\left\{\begin{matrix}A=-\frac{By-C}{x}\text{, }&x\neq 0\\A\in \mathrm{R}\text{, }&C=By\text{ and }x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te By mai i ngā taha e rua.

$$Ax=C-By$$

He hanga arowhānui tō te whārite.

$$xA=C-By$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xA}{x}=\frac{C-By}{x}$$

Mā te whakawehe ki te x ka wetekia te whakareanga ki te x.

$$A=\frac{C-By}{x}$$

Whakaoti mō B

$$\left\{\begin{matrix}B=-\frac{Ax-C}{y}\text{, }&y\neq 0\\B\in \mathrm{R}\text{, }&C=Ax\text{ and }y=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te Ax mai i ngā taha e rua.

$$By=C-Ax$$

He hanga arowhānui tō te whārite.

$$yB=C-Ax$$

Whakawehea ngā taha e rua ki te y.

$$\frac{yB}{y}=\frac{C-Ax}{y}$$

Mā te whakawehe ki te y ka wetekia te whakareanga ki te y.

$$B=\frac{C-Ax}{y}$$