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Whakaoti mō y, x
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y-2x=0
Whakaarohia te whārite tuatahi. Tangohia te 2x mai i ngā taha e rua.
y-2x=0,y+x=6
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.
y-2x=0
Kōwhiria tētahi o ngā whārite ka whakaotia mō te y mā te wehe i te y i te taha mauī o te tohu ōrite.
y=2x
Me tāpiri 2x ki ngā taha e rua o te whārite.
2x+x=6
Whakakapia te 2x mō te y ki tērā atu whārite, y+x=6.
3x=6
Tāpiri 2x ki te x.
x=2
Whakawehea ngā taha e rua ki te 3.
y=2\times 2
Whakaurua te 2 mō x ki y=2x. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
y=4
Whakareatia 2 ki te 2.
y=4,x=2
Kua oti te pūnaha te whakatau.
y-2x=0
Whakaarohia te whārite tuatahi. Tangohia te 2x mai i ngā taha e rua.
y-2x=0,y+x=6
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}1&-2\\1&1\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}0\\6\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}1&-2\\1&1\end{matrix}\right))\left(\begin{matrix}1&-2\\1&1\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-2\\1&1\end{matrix}\right))\left(\begin{matrix}0\\6\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&-2\\1&1\end{matrix}\right).
\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-2\\1&1\end{matrix}\right))\left(\begin{matrix}0\\6\end{matrix}\right)
Ko te hua o tētahi poukapa me te kōaro ko te poukapa tuakiri.
\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-2\\1&1\end{matrix}\right))\left(\begin{matrix}0\\6\end{matrix}\right)
Whakareatia ngā poukapa kei te taha mauī o te tohu ōrite.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{1}{1-\left(-2\right)}&-\frac{-2}{1-\left(-2\right)}\\-\frac{1}{1-\left(-2\right)}&\frac{1}{1-\left(-2\right)}\end{matrix}\right)\left(\begin{matrix}0\\6\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}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{1}{3}&\frac{2}{3}\\-\frac{1}{3}&\frac{1}{3}\end{matrix}\right)\left(\begin{matrix}0\\6\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{2}{3}\times 6\\\frac{1}{3}\times 6\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}4\\2\end{matrix}\right)
Mahia ngā tātaitanga.
y=4,x=2
Tangohia ngā huānga poukapa y me x.
y-2x=0
Whakaarohia te whārite tuatahi. Tangohia te 2x mai i ngā taha e rua.
y-2x=0,y+x=6
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.
y-y-2x-x=-6
Me tango y+x=6 mai i y-2x=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
-2x-x=-6
Tāpiri y ki te -y. Ka whakakore atu ngā kupu y me -y, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
-3x=-6
Tāpiri -2x ki te -x.
x=2
Whakawehea ngā taha e rua ki te -3.
y+2=6
Whakaurua te 2 mō x ki y+x=6. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
y=4
Me tango 2 mai i ngā taha e rua o te whārite.
y=4,x=2
Kua oti te pūnaha te whakatau.