Whakaoti i te {l}{frac{sqrt{3}}{2}T-1/2N=1}{1/2T+frac{sqrt{3}}{2}N=0.5*9.8}

$$\left\{ \begin{array} { l } { \frac { \sqrt { 3 } } { 2 } T - \frac { 1 } { 2 } N = 1 } \\ { \frac { 1 } { 2 } T + \frac { \sqrt { 3 } } { 2 } N = 0.5 \times 9.8 } \end{array} \right.$$

Whakaoti mō T, N

$$T=\frac{\sqrt{3}}{2}+2.45\approx 3.316025404$$

$$N=\frac{49\sqrt{3}}{20}-0.5\approx 3.743524479$$

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.

$$\frac{\sqrt{3}}{2}T-\frac{1}{2}N=1,\frac{1}{2}T+\frac{\sqrt{3}}{2}N=4.9$$

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

$$\frac{\sqrt{3}}{2}T-\frac{1}{2}N=1$$

Me tāpiri \frac{N}{2} ki ngā taha e rua o te whārite.

$$\frac{\sqrt{3}}{2}T=\frac{1}{2}N+1$$

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

$$T=\frac{2\sqrt{3}}{3}\left(\frac{1}{2}N+1\right)$$

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

$$T=\frac{\sqrt{3}}{3}N+\frac{2\sqrt{3}}{3}$$

Whakakapia te \frac{\left(2+N\right)\sqrt{3}}{3} mō te T ki tērā atu whārite, \frac{1}{2}T+\frac{\sqrt{3}}{2}N=4.9.

$$\frac{1}{2}\left(\frac{\sqrt{3}}{3}N+\frac{2\sqrt{3}}{3}\right)+\frac{\sqrt{3}}{2}N=4.9$$

Whakareatia \frac{1}{2} ki te \frac{\left(2+N\right)\sqrt{3}}{3}.

$$\frac{\sqrt{3}}{6}N+\frac{\sqrt{3}}{3}+\frac{\sqrt{3}}{2}N=4.9$$

Tāpiri \frac{\sqrt{3}N}{6} ki te \frac{\sqrt{3}N}{2}.

$$\frac{2\sqrt{3}}{3}N+\frac{\sqrt{3}}{3}=4.9$$

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

$$\frac{2\sqrt{3}}{3}N=-\frac{\sqrt{3}}{3}+\frac{49}{10}$$

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

$$N=\frac{49\sqrt{3}}{20}-\frac{1}{2}$$

Whakaurua te \frac{49\sqrt{3}}{20}-\frac{1}{2} mō N ki T=\frac{\sqrt{3}}{3}N+\frac{2\sqrt{3}}{3}. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō T hāngai tonu.

$$T=\frac{\sqrt{3}}{3}\left(\frac{49\sqrt{3}}{20}-\frac{1}{2}\right)+\frac{2\sqrt{3}}{3}$$

Whakareatia \frac{\sqrt{3}}{3} ki te \frac{49\sqrt{3}}{20}-\frac{1}{2}.

$$T=-\frac{\sqrt{3}}{6}+\frac{49}{20}+\frac{2\sqrt{3}}{3}$$

Tāpiri \frac{2\sqrt{3}}{3} ki te \frac{49}{20}-\frac{\sqrt{3}}{6}.

$$T=\frac{\sqrt{3}}{2}+\frac{49}{20}$$

Kua oti te pūnaha te whakatau.

$$T=\frac{\sqrt{3}}{2}+\frac{49}{20},N=\frac{49\sqrt{3}}{20}-\frac{1}{2}$$

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.

$$\frac{\sqrt{3}}{2}T-\frac{1}{2}N=1,\frac{1}{2}T+\frac{\sqrt{3}}{2}N=4.9$$

Kia ōrite ai a \frac{\sqrt{3}T}{2} me \frac{T}{2}, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te \frac{1}{2} me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te \frac{1}{2}\sqrt{3}.

$$\frac{1}{2}\times \frac{\sqrt{3}}{2}T+\frac{1}{2}\left(-\frac{1}{2}\right)N=\frac{1}{2},\frac{\sqrt{3}}{2}\times \frac{1}{2}T+\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}N=\frac{\sqrt{3}}{2}\times 4.9$$

Whakarūnātia.

$$\frac{\sqrt{3}}{4}T-\frac{1}{4}N=\frac{1}{2},\frac{\sqrt{3}}{4}T+\frac{3}{4}N=\frac{49\sqrt{3}}{20}$$

Me tango \frac{\sqrt{3}}{4}T+\frac{3}{4}N=\frac{49\sqrt{3}}{20} mai i \frac{\sqrt{3}}{4}T-\frac{1}{4}N=\frac{1}{2} mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$\frac{\sqrt{3}}{4}T+\left(-\frac{\sqrt{3}}{4}\right)T-\frac{1}{4}N-\frac{3}{4}N=\frac{1}{2}-\frac{49\sqrt{3}}{20}$$

Tāpiri \frac{\sqrt{3}T}{4} ki te -\frac{\sqrt{3}T}{4}. Ka whakakore atu ngā kupu \frac{\sqrt{3}T}{4} me -\frac{\sqrt{3}T}{4}, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.

$$-\frac{1}{4}N-\frac{3}{4}N=\frac{1}{2}-\frac{49\sqrt{3}}{20}$$

Tāpiri -\frac{N}{4} ki te -\frac{3N}{4}.

$$-N=\frac{1}{2}-\frac{49\sqrt{3}}{20}$$

Tāpiri \frac{1}{2} ki te -\frac{49\sqrt{3}}{20}.

$$-N=-\frac{49\sqrt{3}}{20}+\frac{1}{2}$$

Whakawehea ngā taha e rua ki te -1.

$$N=\frac{49\sqrt{3}}{20}-\frac{1}{2}$$

Whakaurua te -\frac{1}{2}+\frac{49\sqrt{3}}{20} mō N ki \frac{1}{2}T+\frac{\sqrt{3}}{2}N=4.9. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō T hāngai tonu.

$$\frac{1}{2}T+\frac{\sqrt{3}}{2}\left(\frac{49\sqrt{3}}{20}-\frac{1}{2}\right)=4.9$$

Whakareatia \frac{1}{2}\sqrt{3} ki te -\frac{1}{2}+\frac{49\sqrt{3}}{20}.

$$\frac{1}{2}T-\frac{\sqrt{3}}{4}+\frac{147}{40}=4.9$$

Me tango -\frac{\sqrt{3}}{4}+\frac{147}{40} mai i ngā taha e rua o te whārite.

$$\frac{1}{2}T=\frac{\sqrt{3}}{4}+\frac{49}{40}$$

Me whakarea ngā taha e rua ki te 2.

$$T=\frac{\sqrt{3}}{2}+\frac{49}{20}$$

Kua oti te pūnaha te whakatau.

$$T=\frac{\sqrt{3}}{2}+\frac{49}{20},N=\frac{49\sqrt{3}}{20}-\frac{1}{2}$$