Whakaoti i te 53/a+42b=12

$$\frac { 53 } { a } + 42 b = 12$$

Whakaoti mō a

$$a=-\frac{53}{6\left(7b-2\right)}$$

$$b\neq \frac{2}{7}$$

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. Whakareatia ngā taha e rua o te whārite ki te a.

$$53+42ba=12a$$

Tangohia te 12a mai i ngā taha e rua.

$$53+42ba-12a=0$$

Tangohia te 53 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$42ba-12a=-53$$

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

$$\left(42b-12\right)a=-53$$

Whakawehea ngā taha e rua ki te 42b-12.

$$\frac{\left(42b-12\right)a}{42b-12}=-\frac{53}{42b-12}$$

Mā te whakawehe ki te 42b-12 ka wetekia te whakareanga ki te 42b-12.

$$a=-\frac{53}{42b-12}$$

Whakawehe -53 ki te 42b-12.

$$a=-\frac{53}{6\left(7b-2\right)}$$

Tē taea kia ōrite te tāupe a ki 0.

$$a=-\frac{53}{6\left(7b-2\right)}\text{, }a\neq 0$$

Whakaoti mō b

$$b=\frac{2}{7}-\frac{53}{42a}$$

$$a\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te a.

$$53+42ba=12a$$

Tangohia te 53 mai i ngā taha e rua.

$$42ba=12a-53$$

He hanga arowhānui tō te whārite.

$$42ab=12a-53$$

Whakawehea ngā taha e rua ki te 42a.

$$\frac{42ab}{42a}=\frac{12a-53}{42a}$$

Mā te whakawehe ki te 42a ka wetekia te whakareanga ki te 42a.

$$b=\frac{12a-53}{42a}$$

Whakawehe 12a-53 ki te 42a.

$$b=\frac{2}{7}-\frac{53}{42a}$$