Whakaoti i te 7xz+9=yz+3xy

$$7xz+9=yz+3xy$$

Whakaoti mō x

$$\left\{\begin{matrix}x=-\frac{9-yz}{7z-3y}\text{, }&z\neq \frac{3y}{7}\\x\in \mathrm{R}\text{, }&\left(y=-\sqrt{21}\text{ and }z=-\frac{3\sqrt{21}}{7}\right)\text{ or }\left(y=\sqrt{21}\text{ and }z=\frac{3\sqrt{21}}{7}\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te 3xy mai i ngā taha e rua.

$$7xz+9-3xy=yz$$

Tangohia te 9 mai i ngā taha e rua.

$$7xz-3xy=yz-9$$

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

$$\left(7z-3y\right)x=yz-9$$

Whakawehea ngā taha e rua ki te -3y+7z.

$$\frac{\left(7z-3y\right)x}{7z-3y}=\frac{yz-9}{7z-3y}$$

Mā te whakawehe ki te -3y+7z ka wetekia te whakareanga ki te -3y+7z.

$$x=\frac{yz-9}{7z-3y}$$

Whakaoti mō y

$$\left\{\begin{matrix}y=\frac{7xz+9}{3x+z}\text{, }&x\neq -\frac{z}{3}\\y\in \mathrm{R}\text{, }&\left(z=\frac{3\sqrt{21}}{7}\text{ and }x=-\frac{\sqrt{21}}{7}\right)\text{ or }\left(z=-\frac{3\sqrt{21}}{7}\text{ and }x=\frac{\sqrt{21}}{7}\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$yz+3xy=7xz+9$$

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

$$\left(z+3x\right)y=7xz+9$$

He hanga arowhānui tō te whārite.

$$\left(3x+z\right)y=7xz+9$$

Whakawehea ngā taha e rua ki te z+3x.

$$\frac{\left(3x+z\right)y}{3x+z}=\frac{7xz+9}{3x+z}$$

Mā te whakawehe ki te z+3x ka wetekia te whakareanga ki te z+3x.

$$y=\frac{7xz+9}{3x+z}$$