Whakaoti i te 4x=5y+zx

$$4x=5y+zx$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=\frac{5y}{4-z}\text{, }&z\neq 4\\x\in \mathrm{C}\text{, }&y=0\text{ and }z=4\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te zx mai i ngā taha e rua.

$$4x-zx=5y$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(4-z\right)x=5y$$

Whakawehea ngā taha e rua ki te -z+4.

$$\frac{\left(4-z\right)x}{4-z}=\frac{5y}{4-z}$$

Mā te whakawehe ki te -z+4 ka wetekia te whakareanga ki te -z+4.

$$x=\frac{5y}{4-z}$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{5y}{4-z}\text{, }&z\neq 4\\x\in \mathrm{R}\text{, }&y=0\text{ and }z=4\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te zx mai i ngā taha e rua.

$$4x-zx=5y$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(4-z\right)x=5y$$

Whakawehea ngā taha e rua ki te -z+4.

$$\frac{\left(4-z\right)x}{4-z}=\frac{5y}{4-z}$$

Mā te whakawehe ki te -z+4 ka wetekia te whakareanga ki te -z+4.

$$x=\frac{5y}{4-z}$$

Whakaoti mō y

$$y=-\frac{x\left(z-4\right)}{5}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$5y+zx=4x$$

Tangohia te zx mai i ngā taha e rua.

$$5y=4x-zx$$

He hanga arowhānui tō te whārite.

$$5y=4x-xz$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5y}{5}=\frac{x\left(4-z\right)}{5}$$

Mā te whakawehe ki te 5 ka wetekia te whakareanga ki te 5.

$$y=\frac{x\left(4-z\right)}{5}$$

Whakawehe x\left(4-z\right) ki te 5.

$$y=\frac{4x-xz}{5}$$