Whakaoti i te {l}{sqrt{3}x-3y=sqrt{3}}{(x-sqrt{3}y=1)}

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

Whakaoti mō x, y (complex solution)

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

$$y\in \mathrm{C}$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuarua. Whakaraupapatia anō ngā kīanga tau.

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

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.

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

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+\left(-\sqrt{3}\right)y=1.

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

Tāpiri \sqrt{3}y ki te -\sqrt{3}y.

$$1=1$$

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

$$\text{true}$$

Whakaurua te \text{Indeterminate} 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.

$$\text{false}$$

Tāpiri 1 ki te \text{Indeterminate}.

$$x=\text{Indeterminate}$$

Kua oti te pūnaha te whakatau.

$$x=\text{Indeterminate},y=\text{Indeterminate}$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuarua. Whakaraupapatia anō ngā kīanga tau.

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

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.

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

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}.

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

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.

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

Tāpiri \sqrt{3} ki te -\sqrt{3}.

$$\text{true}$$

Whakawehea ngā taha e rua ki te 0.

$$y=\text{Indeterminate}$$

Whakaurua te \text{Indeterminate} mō y ki x+\left(-\sqrt{3}\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.

$$\text{false}$$

Me tango \text{Indeterminate} mai i ngā taha e rua o te whārite.

$$x=\text{Indeterminate}$$

Kua oti te pūnaha te whakatau.

$$x=\text{Indeterminate},y=\text{Indeterminate}$$

Whakaoti mō x, y

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

$$y\in \mathrm{R}$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuarua. Whakaraupapatia anō ngā kīanga tau.

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

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.

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

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+\left(-\sqrt{3}\right)y=1.

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

Tāpiri \sqrt{3}y ki te -\sqrt{3}y.

$$1=1$$

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

$$\text{true}$$

Whakaurua te \text{Indeterminate} 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.

$$x=\text{Indeterminate}$$

Kua oti te pūnaha te whakatau.

$$x=\text{Indeterminate},y=\text{Indeterminate}$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuarua. Whakaraupapatia anō ngā kīanga tau.

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

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.

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

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}.

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

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.

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

Tāpiri \sqrt{3} ki te -\sqrt{3}.

$$\text{true}$$

Whakawehea ngā taha e rua ki te 0.

$$y=\text{Indeterminate}$$

Whakaurua te \text{Indeterminate} mō y ki x+\left(-\sqrt{3}\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.

$$\text{Indeterminate}=1$$

Me tango \text{Indeterminate} mai i ngā taha e rua o te whārite.

$$x=\text{Indeterminate}$$

Kua oti te pūnaha te whakatau.

$$x=\text{Indeterminate},y=\text{Indeterminate}$$