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Whakaoti mō x, y
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3x-y=0
Whakaarohia te whārite tuarua. Tangohia te y mai i ngā taha e rua.
2x+y=10,3x-y=0
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+y=10
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=-y+10
Me tango y mai i ngā taha e rua o te whārite.
x=\frac{1}{2}\left(-y+10\right)
Whakawehea ngā taha e rua ki te 2.
x=-\frac{1}{2}y+5
Whakareatia \frac{1}{2} ki te -y+10.
3\left(-\frac{1}{2}y+5\right)-y=0
Whakakapia te -\frac{y}{2}+5 mō te x ki tērā atu whārite, 3x-y=0.
-\frac{3}{2}y+15-y=0
Whakareatia 3 ki te -\frac{y}{2}+5.
-\frac{5}{2}y+15=0
Tāpiri -\frac{3y}{2} ki te -y.
-\frac{5}{2}y=-15
Me tango 15 mai i ngā taha e rua o te whārite.
y=6
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{1}{2}\times 6+5
Whakaurua te 6 mō y ki x=-\frac{1}{2}y+5. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=-3+5
Whakareatia -\frac{1}{2} ki te 6.
x=2
Tāpiri 5 ki te -3.
x=2,y=6
Kua oti te pūnaha te whakatau.
3x-y=0
Whakaarohia te whārite tuarua. Tangohia te y mai i ngā taha e rua.
2x+y=10,3x-y=0
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}2&1\\3&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}10\\0\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}2&1\\3&-1\end{matrix}\right))\left(\begin{matrix}2&1\\3&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&1\\3&-1\end{matrix}\right))\left(\begin{matrix}10\\0\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}2&1\\3&-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}2&1\\3&-1\end{matrix}\right))\left(\begin{matrix}10\\0\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&1\\3&-1\end{matrix}\right))\left(\begin{matrix}10\\0\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}{2\left(-1\right)-3}&-\frac{1}{2\left(-1\right)-3}\\-\frac{3}{2\left(-1\right)-3}&\frac{2}{2\left(-1\right)-3}\end{matrix}\right)\left(\begin{matrix}10\\0\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}{5}&\frac{1}{5}\\\frac{3}{5}&-\frac{2}{5}\end{matrix}\right)\left(\begin{matrix}10\\0\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{5}\times 10\\\frac{3}{5}\times 10\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}2\\6\end{matrix}\right)
Mahia ngā tātaitanga.
x=2,y=6
Tangohia ngā huānga poukapa x me y.
3x-y=0
Whakaarohia te whārite tuarua. Tangohia te y mai i ngā taha e rua.
2x+y=10,3x-y=0
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+3y=3\times 10,2\times 3x+2\left(-1\right)y=0
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+3y=30,6x-2y=0
Whakarūnātia.
6x-6x+3y+2y=30
Me tango 6x-2y=0 mai i 6x+3y=30 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
3y+2y=30
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=30
Tāpiri 3y ki te 2y.
y=6
Whakawehea ngā taha e rua ki te 5.
3x-6=0
Whakaurua te 6 mō y ki 3x-y=0. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
3x=6
Me tāpiri 6 ki ngā taha e rua o te whārite.
x=2
Whakawehea ngā taha e rua ki te 3.
x=2,y=6
Kua oti te pūnaha te whakatau.