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Whakaoti mō x, y
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2x-3y=0,-x+15y=2
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=0
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
Me tāpiri 3y ki ngā taha e rua o te whārite.
x=\frac{1}{2}\times 3y
Whakawehea ngā taha e rua ki te 2.
x=\frac{3}{2}y
Whakareatia \frac{1}{2} ki te 3y.
-\frac{3}{2}y+15y=2
Whakakapia te \frac{3y}{2} mō te x ki tērā atu whārite, -x+15y=2.
\frac{27}{2}y=2
Tāpiri -\frac{3y}{2} ki te 15y.
y=\frac{4}{27}
Whakawehea ngā taha e rua o te whārite ki te \frac{27}{2}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.
x=\frac{3}{2}\times \frac{4}{27}
Whakaurua te \frac{4}{27} mō y ki x=\frac{3}{2}y. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=\frac{2}{9}
Whakareatia \frac{3}{2} ki te \frac{4}{27} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
x=\frac{2}{9},y=\frac{4}{27}
Kua oti te pūnaha te whakatau.
2x-3y=0,-x+15y=2
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\\-1&15\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}0\\2\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}2&-3\\-1&15\end{matrix}\right))\left(\begin{matrix}2&-3\\-1&15\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&-3\\-1&15\end{matrix}\right))\left(\begin{matrix}0\\2\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}2&-3\\-1&15\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\\-1&15\end{matrix}\right))\left(\begin{matrix}0\\2\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\\-1&15\end{matrix}\right))\left(\begin{matrix}0\\2\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{15}{2\times 15-\left(-3\left(-1\right)\right)}&-\frac{-3}{2\times 15-\left(-3\left(-1\right)\right)}\\-\frac{-1}{2\times 15-\left(-3\left(-1\right)\right)}&\frac{2}{2\times 15-\left(-3\left(-1\right)\right)}\end{matrix}\right)\left(\begin{matrix}0\\2\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{5}{9}&\frac{1}{9}\\\frac{1}{27}&\frac{2}{27}\end{matrix}\right)\left(\begin{matrix}0\\2\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{9}\times 2\\\frac{2}{27}\times 2\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{2}{9}\\\frac{4}{27}\end{matrix}\right)
Mahia ngā tātaitanga.
x=\frac{2}{9},y=\frac{4}{27}
Tangohia ngā huānga poukapa x me y.
2x-3y=0,-x+15y=2
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.
-2x-\left(-3y\right)=0,2\left(-1\right)x+2\times 15y=2\times 2
Kia ōrite ai a 2x me -x, 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 2.
-2x+3y=0,-2x+30y=4
Whakarūnātia.
-2x+2x+3y-30y=-4
Me tango -2x+30y=4 mai i -2x+3y=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
3y-30y=-4
Tāpiri -2x ki te 2x. Ka whakakore atu ngā kupu -2x me 2x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
-27y=-4
Tāpiri 3y ki te -30y.
y=\frac{4}{27}
Whakawehea ngā taha e rua ki te -27.
-x+15\times \frac{4}{27}=2
Whakaurua te \frac{4}{27} mō y ki -x+15y=2. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
-x+\frac{20}{9}=2
Whakareatia 15 ki te \frac{4}{27}.
-x=-\frac{2}{9}
Me tango \frac{20}{9} mai i ngā taha e rua o te whārite.
x=\frac{2}{9}
Whakawehea ngā taha e rua ki te -1.
x=\frac{2}{9},y=\frac{4}{27}
Kua oti te pūnaha te whakatau.