Whakaoti i te {l}{t+2s=-1}{s=t+10}

$$\left. \begin{array} { l } { t + 2 s = - 1 } \\ { s = t + 10 } \end{array} \right.$$

Whakaoti mō t, s

$$t=-7$$

$$s=3$$

Ngā Upane e Whakamahi ana i te Whakakapinga

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

$$s-t=10$$

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.

$$t+2s=-1,-t+s=10$$

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

$$t+2s=-1$$

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

$$t=-2s-1$$

Whakakapia te -2s-1 mō te t ki tērā atu whārite, -t+s=10.

$$-\left(-2s-1\right)+s=10$$

Whakareatia -1 ki te -2s-1.

$$2s+1+s=10$$

Tāpiri 2s ki te s.

$$3s+1=10$$

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

$$3s=9$$

Whakawehea ngā taha e rua ki te 3.

$$s=3$$

Whakaurua te 3 mō s ki t=-2s-1. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō t hāngai tonu.

$$t=-2\times 3-1$$

Whakareatia -2 ki te 3.

$$t=-6-1$$

Tāpiri -1 ki te -6.

$$t=-7$$

Kua oti te pūnaha te whakatau.

$$t=-7,s=3$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

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

$$s-t=10$$

Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.

$$t+2s=-1,-t+s=10$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}1&2\\-1&1\end{matrix}\right)\left(\begin{matrix}t\\s\end{matrix}\right)=\left(\begin{matrix}-1\\10\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&2\\-1&1\end{matrix}\right).

$$inverse(\left(\begin{matrix}1&2\\-1&1\end{matrix}\right))\left(\begin{matrix}1&2\\-1&1\end{matrix}\right)\left(\begin{matrix}t\\s\end{matrix}\right)=inverse(\left(\begin{matrix}1&2\\-1&1\end{matrix}\right))\left(\begin{matrix}-1\\10\end{matrix}\right)$$

Ko te hua o tētahi poukapa me te kōaro ko te poukapa tuakiri.

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}t\\s\end{matrix}\right)=inverse(\left(\begin{matrix}1&2\\-1&1\end{matrix}\right))\left(\begin{matrix}-1\\10\end{matrix}\right)$$

Whakareatia ngā poukapa kei te taha mauī o te tohu ōrite.

$$\left(\begin{matrix}t\\s\end{matrix}\right)=inverse(\left(\begin{matrix}1&2\\-1&1\end{matrix}\right))\left(\begin{matrix}-1\\10\end{matrix}\right)$$

Mō te poukapa 2\times 2 \left(\begin{matrix}a&b\\c&d\end{matrix}\right), ko te \left(\begin{matrix}\frac{d}{ad-bc}&\frac{-b}{ad-bc}\\\frac{-c}{ad-bc}&\frac{a}{ad-bc}\end{matrix}\right) te poukapa kōaro, nō reira ka taea te tuhi anō te whārite poukapa hei rapanga whakarea poukapa.

$$\left(\begin{matrix}t\\s\end{matrix}\right)=\left(\begin{matrix}\frac{1}{1-2\left(-1\right)}&-\frac{2}{1-2\left(-1\right)}\\-\frac{-1}{1-2\left(-1\right)}&\frac{1}{1-2\left(-1\right)}\end{matrix}\right)\left(\begin{matrix}-1\\10\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}t\\s\end{matrix}\right)=\left(\begin{matrix}\frac{1}{3}&-\frac{2}{3}\\\frac{1}{3}&\frac{1}{3}\end{matrix}\right)\left(\begin{matrix}-1\\10\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}t\\s\end{matrix}\right)=\left(\begin{matrix}\frac{1}{3}\left(-1\right)-\frac{2}{3}\times 10\\\frac{1}{3}\left(-1\right)+\frac{1}{3}\times 10\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}t\\s\end{matrix}\right)=\left(\begin{matrix}-7\\3\end{matrix}\right)$$

Tangohia ngā huānga poukapa t me s.

$$t=-7,s=3$$

Ngā Upane e Whakamahi i te Tangohanga

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

$$s-t=10$$

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.

$$t+2s=-1,-t+s=10$$

Kia ōrite ai a t me -t, 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 1.

$$-t-2s=-\left(-1\right),-t+s=10$$

Whakarūnātia.

$$-t-2s=1,-t+s=10$$

Me tango -t+s=10 mai i -t-2s=1 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$-t+t-2s-s=1-10$$

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

$$-2s-s=1-10$$

Tāpiri -2s ki te -s.

$$-3s=1-10$$

Tāpiri 1 ki te -10.

$$-3s=-9$$

Whakawehea ngā taha e rua ki te -3.

$$s=3$$

Whakaurua te 3 mō s ki -t+s=10. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō t hāngai tonu.

$$-t+3=10$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$-t=7$$

Whakawehea ngā taha e rua ki te -1.

$$t=-7$$

Kua oti te pūnaha te whakatau.

$$t=-7,s=3$$