Whakaoti i te {l}{y=sqrt{3}x+5}{x=3+y}

$$\left. \begin{array} { l } { y = \sqrt { 3 } x + 5 } \\ { x = 3 + y } \end{array} \right.$$

Whakaoti mō y, x

$$x=-4\sqrt{3}-4\approx -10.92820323$$

$$y=-4\sqrt{3}-7\approx -13.92820323$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Tangohia te \sqrt{3}x mai i ngā taha e rua.

$$y-\sqrt{3}x=5$$

Whakaraupapatia anō ngā kīanga tau.

$$-\sqrt{3}x+y=5$$

Whakaarohia te whārite tuarua. Tangohia te y mai i ngā taha e rua.

$$x-y=3$$

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.

$$\left(-\sqrt{3}\right)x+y=5,x-y=3$$

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

$$\left(-\sqrt{3}\right)x+y=5$$

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

$$\left(-\sqrt{3}\right)x=-y+5$$

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

$$x=\left(-\frac{\sqrt{3}}{3}\right)\left(-y+5\right)$$

Whakareatia -\frac{\sqrt{3}}{3} ki te -y+5.

$$x=\frac{\sqrt{3}}{3}y-\frac{5\sqrt{3}}{3}$$

Whakakapia te \frac{\left(-5+y\right)\sqrt{3}}{3} mō te x ki tērā atu whārite, x-y=3.

$$\frac{\sqrt{3}}{3}y-\frac{5\sqrt{3}}{3}-y=3$$

Tāpiri \frac{\sqrt{3}y}{3} ki te -y.

$$\left(\frac{\sqrt{3}}{3}-1\right)y-\frac{5\sqrt{3}}{3}=3$$

Me tāpiri \frac{5\sqrt{3}}{3} ki ngā taha e rua o te whārite.

$$\left(\frac{\sqrt{3}}{3}-1\right)y=\frac{5\sqrt{3}}{3}+3$$

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

$$y=-4\sqrt{3}-7$$

Whakaurua te -4\sqrt{3}-7 mō y ki x=\frac{\sqrt{3}}{3}y-\frac{5\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.

$$x=\frac{\sqrt{3}}{3}\left(-4\sqrt{3}-7\right)-\frac{5\sqrt{3}}{3}$$

Whakareatia \frac{\sqrt{3}}{3} ki te -4\sqrt{3}-7.

$$x=-\frac{7\sqrt{3}}{3}-4-\frac{5\sqrt{3}}{3}$$

Tāpiri -\frac{5\sqrt{3}}{3} ki te -4-\frac{7\sqrt{3}}{3}.

$$x=-4\sqrt{3}-4$$

Kua oti te pūnaha te whakatau.

$$x=-4\sqrt{3}-4,y=-4\sqrt{3}-7$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Tangohia te \sqrt{3}x mai i ngā taha e rua.

$$y-\sqrt{3}x=5$$

Whakaraupapatia anō ngā kīanga tau.

$$-\sqrt{3}x+y=5$$

Whakaarohia te whārite tuarua. Tangohia te y mai i ngā taha e rua.

$$x-y=3$$

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.

$$\left(-\sqrt{3}\right)x+y=5,x-y=3$$

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}.

$$\left(-\sqrt{3}\right)x+y=5,\left(-\sqrt{3}\right)x+\left(-\sqrt{3}\right)\left(-1\right)y=\left(-\sqrt{3}\right)\times 3$$

Whakarūnātia.

$$\left(-\sqrt{3}\right)x+y=5,\left(-\sqrt{3}\right)x+\sqrt{3}y=-3\sqrt{3}$$

Me tango \left(-\sqrt{3}\right)x+\sqrt{3}y=-3\sqrt{3} mai i \left(-\sqrt{3}\right)x+y=5 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$\left(-\sqrt{3}\right)x+\sqrt{3}x+y+\left(-\sqrt{3}\right)y=5+3\sqrt{3}$$

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.

$$y+\left(-\sqrt{3}\right)y=5+3\sqrt{3}$$

Tāpiri y ki te -\sqrt{3}y.

$$\left(1-\sqrt{3}\right)y=5+3\sqrt{3}$$

Tāpiri 5 ki te 3\sqrt{3}.

$$\left(1-\sqrt{3}\right)y=3\sqrt{3}+5$$

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

$$y=-4\sqrt{3}-7$$

Whakaurua te -4\sqrt{3}-7 mō y ki x-y=3. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$x-\left(-4\sqrt{3}-7\right)=3$$

Me tango 4\sqrt{3}+7 mai i ngā taha e rua o te whārite.

$$x=-4\sqrt{3}-4$$

Kua oti te pūnaha te whakatau.

$$x=-4\sqrt{3}-4,y=-4\sqrt{3}-7$$