Whakaoti i te 2left(a+b+cright)=(a+b+c)k

$$2 \left( a+b+c \right) =(a+b+c)k$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}\\a=-\left(b+c\right)\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&k=2\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te a+b+c.

$$2a+2b+2c=\left(a+b+c\right)k$$

Whakamahia te āhuatanga tohatoha hei whakarea te a+b+c ki te k.

$$2a+2b+2c=ak+bk+ck$$

Tangohia te ak mai i ngā taha e rua.

$$2a+2b+2c-ak=bk+ck$$

Tangohia te 2b mai i ngā taha e rua.

$$2a+2c-ak=bk+ck-2b$$

Tangohia te 2c mai i ngā taha e rua.

$$2a-ak=bk+ck-2b-2c$$

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

$$\left(2-k\right)a=bk+ck-2b-2c$$

He hanga arowhānui tō te whārite.

$$\left(2-k\right)a=bk-2b+ck-2c$$

Whakawehea ngā taha e rua ki te 2-k.

$$\frac{\left(2-k\right)a}{2-k}=\frac{\left(k-2\right)\left(b+c\right)}{2-k}$$

Mā te whakawehe ki te 2-k ka wetekia te whakareanga ki te 2-k.

$$a=\frac{\left(k-2\right)\left(b+c\right)}{2-k}$$

Whakawehe \left(-2+k\right)\left(b+c\right) ki te 2-k.

$$a=-\left(b+c\right)$$

Whakaoti mō b (complex solution)

$$\left\{\begin{matrix}\\b=-\left(a+c\right)\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&k=2\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te a+b+c.

$$2a+2b+2c=\left(a+b+c\right)k$$

Whakamahia te āhuatanga tohatoha hei whakarea te a+b+c ki te k.

$$2a+2b+2c=ak+bk+ck$$

Tangohia te bk mai i ngā taha e rua.

$$2a+2b+2c-bk=ak+ck$$

Tangohia te 2a mai i ngā taha e rua.

$$2b+2c-bk=ak+ck-2a$$

Tangohia te 2c mai i ngā taha e rua.

$$2b-bk=ak+ck-2a-2c$$

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

$$\left(2-k\right)b=ak+ck-2a-2c$$

He hanga arowhānui tō te whārite.

$$\left(2-k\right)b=ak-2a+ck-2c$$

Whakawehea ngā taha e rua ki te 2-k.

$$\frac{\left(2-k\right)b}{2-k}=\frac{\left(k-2\right)\left(a+c\right)}{2-k}$$

Mā te whakawehe ki te 2-k ka wetekia te whakareanga ki te 2-k.

$$b=\frac{\left(k-2\right)\left(a+c\right)}{2-k}$$

Whakawehe \left(-2+k\right)\left(a+c\right) ki te 2-k.

$$b=-\left(a+c\right)$$

Whakaoti mō a

$$\left\{\begin{matrix}\\a=-\left(b+c\right)\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&k=2\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te a+b+c.

$$2a+2b+2c=\left(a+b+c\right)k$$

Whakamahia te āhuatanga tohatoha hei whakarea te a+b+c ki te k.

$$2a+2b+2c=ak+bk+ck$$

Tangohia te ak mai i ngā taha e rua.

$$2a+2b+2c-ak=bk+ck$$

Tangohia te 2b mai i ngā taha e rua.

$$2a+2c-ak=bk+ck-2b$$

Tangohia te 2c mai i ngā taha e rua.

$$2a-ak=bk+ck-2b-2c$$

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

$$\left(2-k\right)a=bk+ck-2b-2c$$

He hanga arowhānui tō te whārite.

$$\left(2-k\right)a=bk-2b+ck-2c$$

Whakawehea ngā taha e rua ki te 2-k.

$$\frac{\left(2-k\right)a}{2-k}=\frac{\left(k-2\right)\left(b+c\right)}{2-k}$$

Mā te whakawehe ki te 2-k ka wetekia te whakareanga ki te 2-k.

$$a=\frac{\left(k-2\right)\left(b+c\right)}{2-k}$$

Whakawehe \left(-2+k\right)\left(b+c\right) ki te 2-k.

$$a=-\left(b+c\right)$$

Whakaoti mō b

$$\left\{\begin{matrix}\\b=-\left(a+c\right)\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&k=2\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te a+b+c.

$$2a+2b+2c=\left(a+b+c\right)k$$

Whakamahia te āhuatanga tohatoha hei whakarea te a+b+c ki te k.

$$2a+2b+2c=ak+bk+ck$$

Tangohia te bk mai i ngā taha e rua.

$$2a+2b+2c-bk=ak+ck$$

Tangohia te 2a mai i ngā taha e rua.

$$2b+2c-bk=ak+ck-2a$$

Tangohia te 2c mai i ngā taha e rua.

$$2b-bk=ak+ck-2a-2c$$

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

$$\left(2-k\right)b=ak+ck-2a-2c$$

He hanga arowhānui tō te whārite.

$$\left(2-k\right)b=ak-2a+ck-2c$$

Whakawehea ngā taha e rua ki te 2-k.

$$\frac{\left(2-k\right)b}{2-k}=\frac{\left(k-2\right)\left(a+c\right)}{2-k}$$

Mā te whakawehe ki te 2-k ka wetekia te whakareanga ki te 2-k.

$$b=\frac{\left(k-2\right)\left(a+c\right)}{2-k}$$

Whakawehe \left(-2+k\right)\left(a+c\right) ki te 2-k.

$$b=-\left(a+c\right)$$