Whakaoti i te {l}{sqrt{3}x-sqrt{2}y=1}{sqrt{2}x-sqrt{3}y=0}

$$\left\{ \begin{array} { l } { \sqrt { 3 } x - \sqrt { 2 } y = 1 } \\ { \sqrt { 2 } x - \sqrt { 3 } y = 0 } \end{array} \right.$$

Whakaoti mō x, y

$$x=\sqrt{3}\approx 1.732050808$$

$$y=\sqrt{2}\approx 1.414213562$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Whakaraupapatia anō ngā kīanga tau.

$$\sqrt{3}x-\sqrt{2}y=1$$

Whakaarohia te whārite tuarua. Whakaraupapatia anō ngā kīanga tau.

$$\sqrt{2}x-\sqrt{3}y=0$$

Hei whakaoti i ētahi whārite takirua mā te whakakapinga, me whakaoti tētahi whārite i te tuatahi mō tētahi o ngā taurangi. Ka whakakapi i te otinga mō taua taurangi ki tērā o ngā whārite.

$$\sqrt{3}x+\left(-\sqrt{2}\right)y=1,\sqrt{2}x+\left(-\sqrt{3}\right)y=0$$

Kōwhiria tētahi o ngā whārite ka whakaotia mō te x mā te wehe i te x i te taha mauī o te tohu ōrite.

$$\sqrt{3}x+\left(-\sqrt{2}\right)y=1$$

Me tāpiri \sqrt{2}y ki ngā taha e rua o te whārite.

$$\sqrt{3}x=\sqrt{2}y+1$$

Whakawehea ngā taha e rua ki te \sqrt{3}.

$$x=\frac{\sqrt{3}}{3}\left(\sqrt{2}y+1\right)$$

Whakareatia \frac{\sqrt{3}}{3} ki te \sqrt{2}y+1.

$$x=\frac{\sqrt{6}}{3}y+\frac{\sqrt{3}}{3}$$

Whakakapia te \frac{\sqrt{6}y+\sqrt{3}}{3} mō te x ki tērā atu whārite, \sqrt{2}x+\left(-\sqrt{3}\right)y=0.

$$\sqrt{2}\left(\frac{\sqrt{6}}{3}y+\frac{\sqrt{3}}{3}\right)+\left(-\sqrt{3}\right)y=0$$

Whakareatia \sqrt{2} ki te \frac{\sqrt{6}y+\sqrt{3}}{3}.

$$\frac{2\sqrt{3}}{3}y+\frac{\sqrt{6}}{3}+\left(-\sqrt{3}\right)y=0$$

Tāpiri \frac{2\sqrt{3}y}{3} ki te -\sqrt{3}y.

$$\left(-\frac{\sqrt{3}}{3}\right)y+\frac{\sqrt{6}}{3}=0$$

Me tango \frac{\sqrt{6}}{3} mai i ngā taha e rua o te whārite.

$$\left(-\frac{\sqrt{3}}{3}\right)y=-\frac{\sqrt{6}}{3}$$

Whakawehea ngā taha e rua ki te -\frac{\sqrt{3}}{3}.

$$y=\sqrt{2}$$

Whakaurua te \sqrt{2} mō y ki x=\frac{\sqrt{6}}{3}y+\frac{\sqrt{3}}{3}. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$x=\frac{\sqrt{6}}{3}\sqrt{2}+\frac{\sqrt{3}}{3}$$

Whakareatia \frac{\sqrt{6}}{3} ki te \sqrt{2}.

$$x=\frac{2\sqrt{3}+\sqrt{3}}{3}$$

Tāpiri \frac{\sqrt{3}}{3} ki te \frac{2\sqrt{3}}{3}.

$$x=\sqrt{3}$$

Kua oti te pūnaha te whakatau.

$$x=\sqrt{3},y=\sqrt{2}$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Whakaraupapatia anō ngā kīanga tau.

$$\sqrt{3}x-\sqrt{2}y=1$$

Whakaarohia te whārite tuarua. Whakaraupapatia anō ngā kīanga tau.

$$\sqrt{2}x-\sqrt{3}y=0$$

Hei whakaoti mā te tangohanga, ko ngā tau whakarea o tētahi o ngā taurangi me mātua ōrite i ngā whārite e rua kia whakakorehia ai te taurangi ina tangohia tētahi whārite mai i tētahi atu.

$$\sqrt{3}x+\left(-\sqrt{2}\right)y=1,\sqrt{2}x+\left(-\sqrt{3}\right)y=0$$

Kia ōrite ai a \sqrt{3}x me \sqrt{2}x, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te \sqrt{2} me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te \sqrt{3}.

$$\sqrt{2}\sqrt{3}x+\sqrt{2}\left(-\sqrt{2}\right)y=\sqrt{2},\sqrt{3}\sqrt{2}x+\sqrt{3}\left(-\sqrt{3}\right)y=0$$

Whakarūnātia.

$$\sqrt{6}x-2y=\sqrt{2},\sqrt{6}x-3y=0$$

Me tango \sqrt{6}x-3y=0 mai i \sqrt{6}x-2y=\sqrt{2} mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$\sqrt{6}x+\left(-\sqrt{6}\right)x-2y+3y=\sqrt{2}$$

Tāpiri \sqrt{6}x ki te -\sqrt{6}x. Ka whakakore atu ngā kupu \sqrt{6}x me -\sqrt{6}x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.

$$-2y+3y=\sqrt{2}$$

Tāpiri -2y ki te 3y.

$$y=\sqrt{2}$$

Whakaurua te \sqrt{2} mō y ki \sqrt{2}x+\left(-\sqrt{3}\right)y=0. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$\sqrt{2}x+\left(-\sqrt{3}\right)\sqrt{2}=0$$

Whakareatia -\sqrt{3} ki te \sqrt{2}.

$$\sqrt{2}x-\sqrt{6}=0$$

Me tāpiri \sqrt{6} ki ngā taha e rua o te whārite.

$$\sqrt{2}x=\sqrt{6}$$

Whakawehea ngā taha e rua ki te \sqrt{2}.

$$x=\sqrt{3}$$

Kua oti te pūnaha te whakatau.

$$x=\sqrt{3},y=\sqrt{2}$$