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

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

Whakaoti mō x, y

$$x=2\sqrt{3}\approx 3.464101615$$

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

Ngā Upane e Whakamahi ana i te Whakakapinga

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.

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

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

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

Me tāpiri 3y ki ngā taha e rua o te whārite.

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

Whakakapia te 3y-\sqrt{3} mō te x ki tērā atu whārite, -x+2y=0.

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

Whakareatia -1 ki te 3y-\sqrt{3}.

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

Tāpiri -3y ki te 2y.

$$-y+\sqrt{3}=0$$

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

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

Whakawehea ngā taha e rua ki te -1.

$$y=\sqrt{3}$$

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

$$x=3\sqrt{3}-\sqrt{3}$$

Tāpiri -\sqrt{3} ki te 3\sqrt{3}.

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

Kua oti te pūnaha te whakatau.

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

Ngā Upane e Whakamahi i te Tangohanga

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.

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

Kia ōrite ai a x me -x, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te -1 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 1.

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

Whakarūnātia.

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

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

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

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

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

Tāpiri 3y ki te -2y.

$$y=\sqrt{3}$$

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

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

Me tango 2\sqrt{3} mai i ngā taha e rua o te whārite.

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

Whakawehea ngā taha e rua ki te -1.

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

Kua oti te pūnaha te whakatau.

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