Whakaoti i te {l}{xsqrt{3}-3y=sqrt{3}}{x+ysqrt{3}=1}

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

Whakaoti mō x, y

$$x=1$$

$$y=0$$

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.

$$\sqrt{3}x-3y=\sqrt{3},x+\sqrt{3}y=1$$

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

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

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

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

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

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

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

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

Whakakapia te \sqrt{3}y+1 mō te x ki tērā atu whārite, x+\sqrt{3}y=1.

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

Tāpiri \sqrt{3}y ki te \sqrt{3}y.

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

Me tango 1 mai i ngā taha e rua o te whārite.

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

Whakawehea ngā taha e rua ki te 2\sqrt{3}.

$$y=0$$

Whakaurua te 0 mō y ki x=\sqrt{3}y+1. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$x=1$$

Kua oti te pūnaha te whakatau.

$$x=1,y=0$$

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.

$$\sqrt{3}x-3y=\sqrt{3},x+\sqrt{3}y=1$$

Kia ōrite ai a \sqrt{3}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 \sqrt{3}.

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

Whakarūnātia.

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

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

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

Tāpiri \sqrt{3}x ki te -\sqrt{3}x. Ka whakakore atu ngā kupu \sqrt{3}x me -\sqrt{3}x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.

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

Tāpiri -3y ki te -3y.

$$-6y=\sqrt{3}-\sqrt{3}$$

Tāpiri \sqrt{3} ki te -\sqrt{3}.

$$-6y=0$$

Whakawehea ngā taha e rua ki te -6.

$$y=0$$

Whakaurua te 0 mō y ki x+\sqrt{3}y=1. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$x=1$$

Kua oti te pūnaha te whakatau.

$$x=1,y=0$$