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.

$$b=\frac{c-ax}{y}$$