Whakaoti i te {l}{3x-2y=4+3sqrt{3}}{7x-5y=-1,7sqrt{3}}

$$\left\{ \begin{array} { l } { 3 x - 2 y = 4 + 3 \sqrt { 3 } } \\ { 7 x - 5 y = - 1,7 \sqrt { 3 } } \end{array} \right.$$

Whakaoti mō x, y

$$x=\frac{92\sqrt{3}}{5}+20\approx 51.869734859$$

$$y=\frac{261\sqrt{3}}{10}+28\approx 73.206526078$$

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.

$$3x-2y=3\sqrt{3}+4,7x-5y=-\frac{17\sqrt{3}}{10}$$

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

$$3x-2y=3\sqrt{3}+4$$

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

$$3x=2y+3\sqrt{3}+4$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{1}{3}\left(2y+3\sqrt{3}+4\right)$$

Whakareatia \frac{1}{3} ki te 2y+4+3\sqrt{3}.

$$x=\frac{2}{3}y+\sqrt{3}+\frac{4}{3}$$

Whakakapia te \frac{2y}{3}+\frac{4}{3}+\sqrt{3} mō te x ki tērā atu whārite, 7x-5y=-\frac{17\sqrt{3}}{10}.

$$7\left(\frac{2}{3}y+\sqrt{3}+\frac{4}{3}\right)-5y=-\frac{17\sqrt{3}}{10}$$

Whakareatia 7 ki te \frac{2y}{3}+\frac{4}{3}+\sqrt{3}.

$$\frac{14}{3}y+7\sqrt{3}+\frac{28}{3}-5y=-\frac{17\sqrt{3}}{10}$$

Tāpiri \frac{14y}{3} ki te -5y.

$$-\frac{1}{3}y+7\sqrt{3}+\frac{28}{3}=-\frac{17\sqrt{3}}{10}$$

Me tango \frac{28}{3}+7\sqrt{3} mai i ngā taha e rua o te whārite.

$$-\frac{1}{3}y=-\frac{87\sqrt{3}}{10}-\frac{28}{3}$$

Me whakarea ngā taha e rua ki te -3.

$$y=\frac{261\sqrt{3}}{10}+28$$

Whakaurua te \frac{261\sqrt{3}}{10}+28 mō y ki x=\frac{2}{3}y+\sqrt{3}+\frac{4}{3}. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$x=\frac{2}{3}\left(\frac{261\sqrt{3}}{10}+28\right)+\sqrt{3}+\frac{4}{3}$$

Whakareatia \frac{2}{3} ki te \frac{261\sqrt{3}}{10}+28.

$$x=\frac{87\sqrt{3}}{5}+\frac{56}{3}+\sqrt{3}+\frac{4}{3}$$

Tāpiri \frac{4}{3}+\sqrt{3} ki te \frac{87\sqrt{3}}{5}+\frac{56}{3}.

$$x=\frac{92\sqrt{3}}{5}+20$$

Kua oti te pūnaha te whakatau.

$$x=\frac{92\sqrt{3}}{5}+20,y=\frac{261\sqrt{3}}{10}+28$$

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.

$$3x-2y=3\sqrt{3}+4,7x-5y=-\frac{17\sqrt{3}}{10}$$

Kia ōrite ai a 3x me 7x, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te 7 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 3.

$$7\times 3x+7\left(-2\right)y=7\left(3\sqrt{3}+4\right),3\times 7x+3\left(-5\right)y=3\left(-\frac{17\sqrt{3}}{10}\right)$$

Whakarūnātia.

$$21x-14y=21\sqrt{3}+28,21x-15y=-\frac{51\sqrt{3}}{10}$$

Me tango 21x-15y=-\frac{51\sqrt{3}}{10} mai i 21x-14y=21\sqrt{3}+28 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$21x-21x-14y+15y=21\sqrt{3}+28+\frac{51\sqrt{3}}{10}$$

Tāpiri 21x ki te -21x. Ka whakakore atu ngā kupu 21x me -21x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.

$$-14y+15y=21\sqrt{3}+28+\frac{51\sqrt{3}}{10}$$

Tāpiri -14y ki te 15y.

$$y=21\sqrt{3}+28+\frac{51\sqrt{3}}{10}$$

Tāpiri 28+21\sqrt{3} ki te \frac{51\sqrt{3}}{10}.

$$y=\frac{261\sqrt{3}}{10}+28$$

Whakaurua te 28+\frac{261\sqrt{3}}{10} mō y ki 7x-5y=-\frac{17\sqrt{3}}{10}. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$7x-5\left(\frac{261\sqrt{3}}{10}+28\right)=-\frac{17\sqrt{3}}{10}$$

Whakareatia -5 ki te 28+\frac{261\sqrt{3}}{10}.

$$7x-\frac{261\sqrt{3}}{2}-140=-\frac{17\sqrt{3}}{10}$$

Me tango -140-\frac{261\sqrt{3}}{2} mai i ngā taha e rua o te whārite.

$$7x=\frac{644\sqrt{3}}{5}+140$$

Whakawehea ngā taha e rua ki te 7.

$$x=\frac{92\sqrt{3}}{5}+20$$

Kua oti te pūnaha te whakatau.

$$x=\frac{92\sqrt{3}}{5}+20,y=\frac{261\sqrt{3}}{10}+28$$