Whakaoti i te (k-1)x+(2k+1)y-2-k=0

$$( k - 1 ) x + ( 2 k + 1 ) y - 2 - k = 0$$

Whakaoti mō k (complex solution)

$$\left\{\begin{matrix}k=-\frac{-x+y-2}{x+2y-1}\text{, }&x\neq 1-2y\\k\in \mathrm{C}\text{, }&x=-1\text{ and }y=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te k-1 ki te x.

$$kx-x+\left(2k+1\right)y-2-k=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2k+1 ki te y.

$$kx-x+2ky+y-2-k=0$$

Me tāpiri te x ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$kx+2ky+y-2-k=x$$

Tangohia te y mai i ngā taha e rua.

$$kx+2ky-2-k=x-y$$

Me tāpiri te 2 ki ngā taha e rua.

$$kx+2ky-k=x-y+2$$

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

$$\left(x+2y-1\right)k=x-y+2$$

Whakawehea ngā taha e rua ki te x+2y-1.

$$\frac{\left(x+2y-1\right)k}{x+2y-1}=\frac{x-y+2}{x+2y-1}$$

Mā te whakawehe ki te x+2y-1 ka wetekia te whakareanga ki te x+2y-1.

$$k=\frac{x-y+2}{x+2y-1}$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=-\frac{2ky+y-k-2}{k-1}\text{, }&k\neq 1\\x\in \mathrm{C}\text{, }&y=1\text{ and }k=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te k-1 ki te x.

$$kx-x+\left(2k+1\right)y-2-k=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2k+1 ki te y.

$$kx-x+2ky+y-2-k=0$$

Tangohia te 2ky mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$kx-x+y-2-k=-2ky$$

Tangohia te y mai i ngā taha e rua.

$$kx-x-2-k=-2ky-y$$

Me tāpiri te 2 ki ngā taha e rua.

$$kx-x-k=-2ky-y+2$$

Me tāpiri te k ki ngā taha e rua.

$$kx-x=-2ky-y+2+k$$

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

$$\left(k-1\right)x=-2ky-y+2+k$$

He hanga arowhānui tō te whārite.

$$\left(k-1\right)x=2+k-y-2ky$$

Whakawehea ngā taha e rua ki te k-1.

$$\frac{\left(k-1\right)x}{k-1}=\frac{2+k-y-2ky}{k-1}$$

Mā te whakawehe ki te k-1 ka wetekia te whakareanga ki te k-1.

$$x=\frac{2+k-y-2ky}{k-1}$$

Whakaoti mō k

$$\left\{\begin{matrix}k=-\frac{-x+y-2}{x+2y-1}\text{, }&x\neq 1-2y\\k\in \mathrm{R}\text{, }&x=-1\text{ and }y=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te k-1 ki te x.

$$kx-x+\left(2k+1\right)y-2-k=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2k+1 ki te y.

$$kx-x+2ky+y-2-k=0$$

Me tāpiri te x ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$kx+2ky+y-2-k=x$$

Tangohia te y mai i ngā taha e rua.

$$kx+2ky-2-k=x-y$$

Me tāpiri te 2 ki ngā taha e rua.

$$kx+2ky-k=x-y+2$$

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

$$\left(x+2y-1\right)k=x-y+2$$

Whakawehea ngā taha e rua ki te x+2y-1.

$$\frac{\left(x+2y-1\right)k}{x+2y-1}=\frac{x-y+2}{x+2y-1}$$

Mā te whakawehe ki te x+2y-1 ka wetekia te whakareanga ki te x+2y-1.

$$k=\frac{x-y+2}{x+2y-1}$$

Whakaoti mō x

$$\left\{\begin{matrix}x=-\frac{2ky+y-k-2}{k-1}\text{, }&k\neq 1\\x\in \mathrm{R}\text{, }&y=1\text{ and }k=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te k-1 ki te x.

$$kx-x+\left(2k+1\right)y-2-k=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2k+1 ki te y.

$$kx-x+2ky+y-2-k=0$$

Tangohia te 2ky mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$kx-x+y-2-k=-2ky$$

Tangohia te y mai i ngā taha e rua.

$$kx-x-2-k=-2ky-y$$

Me tāpiri te 2 ki ngā taha e rua.

$$kx-x-k=-2ky-y+2$$

Me tāpiri te k ki ngā taha e rua.

$$kx-x=-2ky-y+2+k$$

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

$$\left(k-1\right)x=-2ky-y+2+k$$

He hanga arowhānui tō te whārite.

$$\left(k-1\right)x=2+k-y-2ky$$

Whakawehea ngā taha e rua ki te k-1.

$$\frac{\left(k-1\right)x}{k-1}=\frac{2+k-y-2ky}{k-1}$$

Mā te whakawehe ki te k-1 ka wetekia te whakareanga ki te k-1.

$$x=\frac{2+k-y-2ky}{k-1}$$