Whakaoti i te z=ax+by

$$z = a x + b y$$

Whakaoti mō a

$$\left\{\begin{matrix}a=-\frac{by-z}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&z=by\text{ and }x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$ax+by=z$$

Tangohia te by mai i ngā taha e rua.

$$ax=z-by$$

He hanga arowhānui tō te whārite.

$$xa=z-by$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xa}{x}=\frac{z-by}{x}$$

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

$$a=\frac{z-by}{x}$$

Whakaoti mō b

$$\left\{\begin{matrix}b=-\frac{ax-z}{y}\text{, }&y\neq 0\\b\in \mathrm{R}\text{, }&z=ax\text{ and }y=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$ax+by=z$$

Tangohia te ax mai i ngā taha e rua.

$$by=z-ax$$

He hanga arowhānui tō te whārite.

$$yb=z-ax$$

Whakawehea ngā taha e rua ki te y.

$$\frac{yb}{y}=\frac{z-ax}{y}$$

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

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