Whakaoti i te 18*(09*65x-35)+42*(y/10*100-50)=810

$$18 \cdot ( 09 \times 65 x - 35 ) + 42 \cdot ( \frac { y } { 10 } \cdot 100 - 50 ) = 810$$

Whakaoti mō y

$$y = \frac{59}{7} = 8\frac{3}{7} = 8.428571428571429$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 10.

$$180\left(0\times 9\times 65x-35\right)+420\left(\frac{y}{10}\times 100-50\right)=8100$$

Whakareatia te 0 ki te 9, ka 0.

$$180\left(0\times 65x-35\right)+420\left(\frac{y}{10}\times 100-50\right)=8100$$

Whakareatia te 0 ki te 65, ka 0.

$$180\left(0x-35\right)+420\left(\frac{y}{10}\times 100-50\right)=8100$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$180\left(0-35\right)+420\left(\frac{y}{10}\times 100-50\right)=8100$$

Tangohia te 35 i te 0, ka -35.

$$180\left(-35\right)+420\left(\frac{y}{10}\times 100-50\right)=8100$$

Whakareatia te 180 ki te -35, ka -6300.

$$-6300+420\left(\frac{y}{10}\times 100-50\right)=8100$$

Whakakorea atu te tauwehe pūnoa nui rawa 10 i roto i te 100 me te 10.

$$-6300+420\left(10y-50\right)=8100$$

Whakamahia te āhuatanga tohatoha hei whakarea te 420 ki te 10y-50.

$$-6300+4200y-21000=8100$$

Tangohia te 21000 i te -6300, ka -27300.

$$-27300+4200y=8100$$

Me tāpiri te 27300 ki ngā taha e rua.

$$4200y=8100+27300$$

Tāpirihia te 8100 ki te 27300, ka 35400.

$$4200y=35400$$

Whakawehea ngā taha e rua ki te 4200.

$$y=\frac{35400}{4200}$$

Whakahekea te hautanga \frac{35400}{4200} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 600.

$$y=\frac{59}{7}$$

Whakaoti mō x (complex solution)

$$x\in \mathrm{C}$$

$$y = \frac{59}{7} = 8\frac{3}{7} = 8.428571428571429$$

Whakaoti mō x

$$x\in \mathrm{R}$$

$$y = \frac{59}{7} = 8\frac{3}{7} = 8.428571428571429$$