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m+n=-3,-3m+2n=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.
m+n=-3
Kōwhiria tētahi o ngā whārite ka whakaotia mō te m mā te wehe i te m i te taha mauī o te tohu ōrite.
m=-n-3
Me tango n mai i ngā taha e rua o te whārite.
-3\left(-n-3\right)+2n=1
Whakakapia te -n-3 mō te m ki tērā atu whārite, -3m+2n=1.
3n+9+2n=1
Whakareatia -3 ki te -n-3.
5n+9=1
Tāpiri 3n ki te 2n.
5n=-8
Me tango 9 mai i ngā taha e rua o te whārite.
n=-\frac{8}{5}
Whakawehea ngā taha e rua ki te 5.
m=-\left(-\frac{8}{5}\right)-3
Whakaurua te -\frac{8}{5} mō n ki m=-n-3. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō m hāngai tonu.
m=\frac{8}{5}-3
Whakareatia -1 ki te -\frac{8}{5}.
m=-\frac{7}{5}
Tāpiri -3 ki te \frac{8}{5}.
m=-\frac{7}{5},n=-\frac{8}{5}
Kua oti te pūnaha te whakatau.
m+n=-3,-3m+2n=1
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}1&1\\-3&2\end{matrix}\right)\left(\begin{matrix}m\\n\end{matrix}\right)=\left(\begin{matrix}-3\\1\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}1&1\\-3&2\end{matrix}\right))\left(\begin{matrix}1&1\\-3&2\end{matrix}\right)\left(\begin{matrix}m\\n\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\-3&2\end{matrix}\right))\left(\begin{matrix}-3\\1\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&1\\-3&2\end{matrix}\right).
\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}m\\n\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\-3&2\end{matrix}\right))\left(\begin{matrix}-3\\1\end{matrix}\right)
Ko te hua o tētahi poukapa me te kōaro ko te poukapa tuakiri.
\left(\begin{matrix}m\\n\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\-3&2\end{matrix}\right))\left(\begin{matrix}-3\\1\end{matrix}\right)
Whakareatia ngā poukapa kei te taha mauī o te tohu ōrite.
\left(\begin{matrix}m\\n\end{matrix}\right)=\left(\begin{matrix}\frac{2}{2-\left(-3\right)}&-\frac{1}{2-\left(-3\right)}\\-\frac{-3}{2-\left(-3\right)}&\frac{1}{2-\left(-3\right)}\end{matrix}\right)\left(\begin{matrix}-3\\1\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}m\\n\end{matrix}\right)=\left(\begin{matrix}\frac{2}{5}&-\frac{1}{5}\\\frac{3}{5}&\frac{1}{5}\end{matrix}\right)\left(\begin{matrix}-3\\1\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}m\\n\end{matrix}\right)=\left(\begin{matrix}\frac{2}{5}\left(-3\right)-\frac{1}{5}\\\frac{3}{5}\left(-3\right)+\frac{1}{5}\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}m\\n\end{matrix}\right)=\left(\begin{matrix}-\frac{7}{5}\\-\frac{8}{5}\end{matrix}\right)
Mahia ngā tātaitanga.
m=-\frac{7}{5},n=-\frac{8}{5}
Tangohia ngā huānga poukapa m me n.
m+n=-3,-3m+2n=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.
-3m-3n=-3\left(-3\right),-3m+2n=1
Kia ōrite ai a m me -3m, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te -3 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 1.
-3m-3n=9,-3m+2n=1
Whakarūnātia.
-3m+3m-3n-2n=9-1
Me tango -3m+2n=1 mai i -3m-3n=9 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
-3n-2n=9-1
Tāpiri -3m ki te 3m. Ka whakakore atu ngā kupu -3m me 3m, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
-5n=9-1
Tāpiri -3n ki te -2n.
-5n=8
Tāpiri 9 ki te -1.
n=-\frac{8}{5}
Whakawehea ngā taha e rua ki te -5.
-3m+2\left(-\frac{8}{5}\right)=1
Whakaurua te -\frac{8}{5} mō n ki -3m+2n=1. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō m hāngai tonu.
-3m-\frac{16}{5}=1
Whakareatia 2 ki te -\frac{8}{5}.
-3m=\frac{21}{5}
Me tāpiri \frac{16}{5} ki ngā taha e rua o te whārite.
m=-\frac{7}{5}
Whakawehea ngā taha e rua ki te -3.
m=-\frac{7}{5},n=-\frac{8}{5}
Kua oti te pūnaha te whakatau.