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Whakaoti mō x, y
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x+3y=14,4x-y=4
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.
x+3y=14
Kōwhiria tētahi o ngā whārite ka whakaotia mō te x mā te wehe i te x i te taha mauī o te tohu ōrite.
x=-3y+14
Me tango 3y mai i ngā taha e rua o te whārite.
4\left(-3y+14\right)-y=4
Whakakapia te -3y+14 mō te x ki tērā atu whārite, 4x-y=4.
-12y+56-y=4
Whakareatia 4 ki te -3y+14.
-13y+56=4
Tāpiri -12y ki te -y.
-13y=-52
Me tango 56 mai i ngā taha e rua o te whārite.
y=4
Whakawehea ngā taha e rua ki te -13.
x=-3\times 4+14
Whakaurua te 4 mō y ki x=-3y+14. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=-12+14
Whakareatia -3 ki te 4.
x=2
Tāpiri 14 ki te -12.
x=2,y=4
Kua oti te pūnaha te whakatau.
x+3y=14,4x-y=4
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}1&3\\4&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}14\\4\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}1&3\\4&-1\end{matrix}\right))\left(\begin{matrix}1&3\\4&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&3\\4&-1\end{matrix}\right))\left(\begin{matrix}14\\4\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&3\\4&-1\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}1&3\\4&-1\end{matrix}\right))\left(\begin{matrix}14\\4\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}1&3\\4&-1\end{matrix}\right))\left(\begin{matrix}14\\4\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{1}{-1-3\times 4}&-\frac{3}{-1-3\times 4}\\-\frac{4}{-1-3\times 4}&\frac{1}{-1-3\times 4}\end{matrix}\right)\left(\begin{matrix}14\\4\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}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{13}&\frac{3}{13}\\\frac{4}{13}&-\frac{1}{13}\end{matrix}\right)\left(\begin{matrix}14\\4\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{13}\times 14+\frac{3}{13}\times 4\\\frac{4}{13}\times 14-\frac{1}{13}\times 4\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}2\\4\end{matrix}\right)
Mahia ngā tātaitanga.
x=2,y=4
Tangohia ngā huānga poukapa x me y.
x+3y=14,4x-y=4
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.
4x+4\times 3y=4\times 14,4x-y=4
Kia ōrite ai a x me 4x, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te 4 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 1.
4x+12y=56,4x-y=4
Whakarūnātia.
4x-4x+12y+y=56-4
Me tango 4x-y=4 mai i 4x+12y=56 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
12y+y=56-4
Tāpiri 4x ki te -4x. Ka whakakore atu ngā kupu 4x me -4x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
13y=56-4
Tāpiri 12y ki te y.
13y=52
Tāpiri 56 ki te -4.
y=4
Whakawehea ngā taha e rua ki te 13.
4x-4=4
Whakaurua te 4 mō y ki 4x-y=4. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
4x=8
Me tāpiri 4 ki ngā taha e rua o te whārite.
x=2
Whakawehea ngā taha e rua ki te 4.
x=2,y=4
Kua oti te pūnaha te whakatau.