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2x+3y=12,3x+2y=13
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.
2x+3y=12
Kōwhiria tētahi o ngā whārite ka whakaotia mō te x mā te wehe i te x i te taha mauī o te tohu ōrite.
2x=-3y+12
Me tango 3y mai i ngā taha e rua o te whārite.
x=\frac{1}{2}\left(-3y+12\right)
Whakawehea ngā taha e rua ki te 2.
x=-\frac{3}{2}y+6
Whakareatia \frac{1}{2} ki te -3y+12.
3\left(-\frac{3}{2}y+6\right)+2y=13
Whakakapia te -\frac{3y}{2}+6 mō te x ki tērā atu whārite, 3x+2y=13.
-\frac{9}{2}y+18+2y=13
Whakareatia 3 ki te -\frac{3y}{2}+6.
-\frac{5}{2}y+18=13
Tāpiri -\frac{9y}{2} ki te 2y.
-\frac{5}{2}y=-5
Me tango 18 mai i ngā taha e rua o te whārite.
y=2
Whakawehea ngā taha e rua o te whārite ki te -\frac{5}{2}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.
x=-\frac{3}{2}\times 2+6
Whakaurua te 2 mō y ki x=-\frac{3}{2}y+6. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=-3+6
Whakareatia -\frac{3}{2} ki te 2.
x=3
Tāpiri 6 ki te -3.
x=3,y=2
Kua oti te pūnaha te whakatau.
2x+3y=12,3x+2y=13
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}2&3\\3&2\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}12\\13\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}2&3\\3&2\end{matrix}\right))\left(\begin{matrix}2&3\\3&2\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&3\\3&2\end{matrix}\right))\left(\begin{matrix}12\\13\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}2&3\\3&2\end{matrix}\right).
\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&3\\3&2\end{matrix}\right))\left(\begin{matrix}12\\13\end{matrix}\right)
Ko te hua o tētahi poukapa me te kōaro ko te poukapa tuakiri.
\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&3\\3&2\end{matrix}\right))\left(\begin{matrix}12\\13\end{matrix}\right)
Whakareatia ngā poukapa kei te taha mauī o te tohu ōrite.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{2}{2\times 2-3\times 3}&-\frac{3}{2\times 2-3\times 3}\\-\frac{3}{2\times 2-3\times 3}&\frac{2}{2\times 2-3\times 3}\end{matrix}\right)\left(\begin{matrix}12\\13\end{matrix}\right)
Mō te poukapa 2\times 2 \left(\begin{matrix}a&b\\c&d\end{matrix}\right), ko te poukapa kōaro ko \left(\begin{matrix}\frac{d}{ad-bc}&\frac{-b}{ad-bc}\\\frac{-c}{ad-bc}&\frac{a}{ad-bc}\end{matrix}\right), kia tuhia anō ai te whārite poukapa hei rapanga whakarea poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{2}{5}&\frac{3}{5}\\\frac{3}{5}&-\frac{2}{5}\end{matrix}\right)\left(\begin{matrix}12\\13\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{2}{5}\times 12+\frac{3}{5}\times 13\\\frac{3}{5}\times 12-\frac{2}{5}\times 13\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}3\\2\end{matrix}\right)
Mahia ngā tātaitanga.
x=3,y=2
Tangohia ngā huānga poukapa x me y.
2x+3y=12,3x+2y=13
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.
3\times 2x+3\times 3y=3\times 12,2\times 3x+2\times 2y=2\times 13
Kia ōrite ai a 2x me 3x, 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 2.
6x+9y=36,6x+4y=26
Whakarūnātia.
6x-6x+9y-4y=36-26
Me tango 6x+4y=26 mai i 6x+9y=36 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
9y-4y=36-26
Tāpiri 6x ki te -6x. Ka whakakore atu ngā kupu 6x me -6x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
5y=36-26
Tāpiri 9y ki te -4y.
5y=10
Tāpiri 36 ki te -26.
y=2
Whakawehea ngā taha e rua ki te 5.
3x+2\times 2=13
Whakaurua te 2 mō y ki 3x+2y=13. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
3x+4=13
Whakareatia 2 ki te 2.
3x=9
Me tango 4 mai i ngā taha e rua o te whārite.
x=3
Whakawehea ngā taha e rua ki te 3.
x=3,y=2
Kua oti te pūnaha te whakatau.