Whakaoti i te a+b/2a-3b=3b-a/6a

$$\frac { a + b } { 2 a } - 3 b = \frac { 3 b - a } { 6 a }$$

Whakaoti mō a

$$a\neq 0$$

$$b=\frac{2}{9}\text{ and }a\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe a ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 6a, arā, te tauraro pātahi he tino iti rawa te kitea o 2a,6a.

$$3\left(a+b\right)-3b\times 6a=3b-a$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te a+b.

$$3a+3b-3b\times 6a=3b-a$$

Whakareatia te -3 ki te 6, ka -18.

$$3a+3b-18ba=3b-a$$

Me tāpiri te a ki ngā taha e rua.

$$3a+3b-18ba+a=3b$$

Pahekotia te 3a me a, ka 4a.

$$4a+3b-18ba=3b$$

Tangohia te 3b mai i ngā taha e rua.

$$4a-18ba=3b-3b$$

Pahekotia te 3b me -3b, ka 0.

$$4a-18ba=0$$

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

$$\left(4-18b\right)a=0$$

Whakawehe 0 ki te 4-18b.

$$a=0$$

Tē taea kia ōrite te tāupe a ki 0.

$$a\in \emptyset$$

Whakaoti mō b

$$b = \frac{2}{9} = 0.2222222222222222$$

$$a\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 6a, arā, te tauraro pātahi he tino iti rawa te kitea o 2a,6a.

$$3\left(a+b\right)-3b\times 6a=3b-a$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te a+b.

$$3a+3b-3b\times 6a=3b-a$$

Whakareatia te -3 ki te 6, ka -18.

$$3a+3b-18ba=3b-a$$

Tangohia te 3b mai i ngā taha e rua.

$$3a+3b-18ba-3b=-a$$

Pahekotia te 3b me -3b, ka 0.

$$3a-18ba=-a$$

Tangohia te 3a mai i ngā taha e rua.

$$-18ba=-a-3a$$

Pahekotia te -a me -3a, ka -4a.

$$-18ba=-4a$$

He hanga arowhānui tō te whārite.

$$\left(-18a\right)b=-4a$$

Whakawehea ngā taha e rua ki te -18a.

$$\frac{\left(-18a\right)b}{-18a}=-\frac{4a}{-18a}$$

Mā te whakawehe ki te -18a ka wetekia te whakareanga ki te -18a.

$$b=-\frac{4a}{-18a}$$

Whakawehe -4a ki te -18a.

$$b=\frac{2}{9}$$