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

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

Whakaoti mō x, y

$$x=\sqrt{3}-1\approx 0.732050808$$

$$y=-2$$

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.

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

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

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

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

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

Whakawehea ngā taha e rua ki te 2.

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

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

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

Whakakapia te -\frac{\sqrt{3}y}{2}-1 mō te x ki tērā atu whārite, x-y-1=\sqrt{3}.

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

Tāpiri -\frac{\sqrt{3}y}{2} ki te -y.

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

Tāpiri -1 ki te -1.

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

Me tāpiri 2 ki ngā taha e rua o te whārite.

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

Whakawehea ngā taha e rua ki te -\frac{\sqrt{3}}{2}-1.

$$y=-2$$

Whakaurua te -2 mō y ki x=\left(-\frac{\sqrt{3}}{2}\right)y-1. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

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

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

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

Kua oti te pūnaha te whakatau.

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

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.

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

Kia ōrite ai a 2x 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 2.

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

Whakarūnātia.

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

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

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

Tāpiri 2x ki te -2x. Ka whakakore atu ngā kupu 2x me -2x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.

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

Tāpiri \sqrt{3}y ki te 2y.

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

Tāpiri -2 ki te -2\sqrt{3}.

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

Me tango 2 mai i ngā taha e rua o te whārite.

$$\left(\sqrt{3}+2\right)y=-2\sqrt{3}-4$$

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

$$y=-2$$

Whakaurua te -2 mō y ki x-y-1=\sqrt{3}. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

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

Tāpiri 2 ki te -1.

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

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

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

Kua oti te pūnaha te whakatau.

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