Whakaoti i te 1/x+1/2y=8.quad1/2x-1/y=-1

$$\frac { 1 } { x } + \frac { 1 } { 2 y } = 8 . \quad \frac { 1 } { 2 x } - \frac { 1 } { y } = - 1$$

Whakaoti mō x

$$x=-\frac{2y}{1-16y}$$

$$y\neq 0\text{ and }y\neq \frac{1}{16}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$2y+x=16xy$$

Tangohia te 16xy mai i ngā taha e rua.

$$2y+x-16xy=0$$

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

$$x-16xy=-2y$$

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

$$\left(1-16y\right)x=-2y$$

Whakawehea ngā taha e rua ki te 1-16y.

$$\frac{\left(1-16y\right)x}{1-16y}=-\frac{2y}{1-16y}$$

Mā te whakawehe ki te 1-16y ka wetekia te whakareanga ki te 1-16y.

$$x=-\frac{2y}{1-16y}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{2y}{1-16y}\text{, }x\neq 0$$

Whakaoti mō y

$$y=-\frac{x}{2\left(1-8x\right)}$$

$$x\neq 0\text{ and }x\neq \frac{1}{8}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$2y+x=16xy$$

Tangohia te 16xy mai i ngā taha e rua.

$$2y+x-16xy=0$$

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

$$2y-16xy=-x$$

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

$$\left(2-16x\right)y=-x$$

Whakawehea ngā taha e rua ki te 2-16x.

$$\frac{\left(2-16x\right)y}{2-16x}=-\frac{x}{2-16x}$$

Mā te whakawehe ki te 2-16x ka wetekia te whakareanga ki te 2-16x.

$$y=-\frac{x}{2-16x}$$

Whakawehe -x ki te 2-16x.

$$y=-\frac{x}{2\left(1-8x\right)}$$

Tē taea kia ōrite te tāupe y ki 0.

$$y=-\frac{x}{2\left(1-8x\right)}\text{, }y\neq 0$$