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Whakaoti mō y, x
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y-x=-7
Whakaarohia te whārite tuatahi. Tangohia te x mai i ngā taha e rua.
y+2x=-1
Whakaarohia te whārite tuarua. Me tāpiri te 2x ki ngā taha e rua.
y-x=-7,y+2x=-1
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-x=-7
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=x-7
Me tāpiri x ki ngā taha e rua o te whārite.
x-7+2x=-1
Whakakapia te x-7 mō te y ki tērā atu whārite, y+2x=-1.
3x-7=-1
Tāpiri x ki te 2x.
3x=6
Me tāpiri 7 ki ngā taha e rua o te whārite.
x=2
Whakawehea ngā taha e rua ki te 3.
y=2-7
Whakaurua te 2 mō x ki y=x-7. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
y=-5
Tāpiri -7 ki te 2.
y=-5,x=2
Kua oti te pūnaha te whakatau.
y-x=-7
Whakaarohia te whārite tuatahi. Tangohia te x mai i ngā taha e rua.
y+2x=-1
Whakaarohia te whārite tuarua. Me tāpiri te 2x ki ngā taha e rua.
y-x=-7,y+2x=-1
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}y\\x\end{matrix}\right)=\left(\begin{matrix}-7\\-1\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}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-1\\1&2\end{matrix}\right))\left(\begin{matrix}-7\\-1\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}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-1\\1&2\end{matrix}\right))\left(\begin{matrix}-7\\-1\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&-1\\1&2\end{matrix}\right))\left(\begin{matrix}-7\\-1\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{2}{2-\left(-1\right)}&-\frac{-1}{2-\left(-1\right)}\\-\frac{1}{2-\left(-1\right)}&\frac{1}{2-\left(-1\right)}\end{matrix}\right)\left(\begin{matrix}-7\\-1\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}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{2}{3}&\frac{1}{3}\\-\frac{1}{3}&\frac{1}{3}\end{matrix}\right)\left(\begin{matrix}-7\\-1\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{2}{3}\left(-7\right)+\frac{1}{3}\left(-1\right)\\-\frac{1}{3}\left(-7\right)+\frac{1}{3}\left(-1\right)\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-5\\2\end{matrix}\right)
Mahia ngā tātaitanga.
y=-5,x=2
Tangohia ngā huānga poukapa y me x.
y-x=-7
Whakaarohia te whārite tuatahi. Tangohia te x mai i ngā taha e rua.
y+2x=-1
Whakaarohia te whārite tuarua. Me tāpiri te 2x ki ngā taha e rua.
y-x=-7,y+2x=-1
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-x-2x=-7+1
Me tango y+2x=-1 mai i y-x=-7 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
-x-2x=-7+1
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=-7+1
Tāpiri -x ki te -2x.
-3x=-6
Tāpiri -7 ki te 1.
x=2
Whakawehea ngā taha e rua ki te -3.
y+2\times 2=-1
Whakaurua te 2 mō x ki y+2x=-1. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
y+4=-1
Whakareatia 2 ki te 2.
y=-5
Me tango 4 mai i ngā taha e rua o te whārite.
y=-5,x=2
Kua oti te pūnaha te whakatau.