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Whakaoti mō x, y
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x+y=3,x-2y=-3
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+y=3
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=-y+3
Me tango y mai i ngā taha e rua o te whārite.
-y+3-2y=-3
Whakakapia te -y+3 mō te x ki tērā atu whārite, x-2y=-3.
-3y+3=-3
Tāpiri -y ki te -2y.
-3y=-6
Me tango 3 mai i ngā taha e rua o te whārite.
y=2
Whakawehea ngā taha e rua ki te -3.
x=-2+3
Whakaurua te 2 mō y ki x=-y+3. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=1
Tāpiri 3 ki te -2.
x=1,y=2
Kua oti te pūnaha te whakatau.
x+y=3,x-2y=-3
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\\1&-2\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}3\\-3\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}1&1\\1&-2\end{matrix}\right))\left(\begin{matrix}1&1\\1&-2\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\1&-2\end{matrix}\right))\left(\begin{matrix}3\\-3\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&1\\1&-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}1&1\\1&-2\end{matrix}\right))\left(\begin{matrix}3\\-3\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&1\\1&-2\end{matrix}\right))\left(\begin{matrix}3\\-3\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}{-2-1}&-\frac{1}{-2-1}\\-\frac{1}{-2-1}&\frac{1}{-2-1}\end{matrix}\right)\left(\begin{matrix}3\\-3\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{2}{3}&\frac{1}{3}\\\frac{1}{3}&-\frac{1}{3}\end{matrix}\right)\left(\begin{matrix}3\\-3\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{2}{3}\times 3+\frac{1}{3}\left(-3\right)\\\frac{1}{3}\times 3-\frac{1}{3}\left(-3\right)\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}1\\2\end{matrix}\right)
Mahia ngā tātaitanga.
x=1,y=2
Tangohia ngā huānga poukapa x me y.
x+y=3,x-2y=-3
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.
x-x+y+2y=3+3
Me tango x-2y=-3 mai i x+y=3 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
y+2y=3+3
Tāpiri x ki te -x. Ka whakakore atu ngā kupu x me -x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
3y=3+3
Tāpiri y ki te 2y.
3y=6
Tāpiri 3 ki te 3.
y=2
Whakawehea ngā taha e rua ki te 3.
x-2\times 2=-3
Whakaurua te 2 mō y ki x-2y=-3. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x-4=-3
Whakareatia -2 ki te 2.
x=1
Me tāpiri 4 ki ngā taha e rua o te whārite.
x=1,y=2
Kua oti te pūnaha te whakatau.