Whakaoti mō y, x
x=6
y=-4
Graph
Tohaina
Kua tāruatia ki te papatopenga
y+x=2
Whakaarohia te whārite tuatahi. Me tāpiri te x ki ngā taha e rua.
y+x=2,-2y+x=14
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=2
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+2
Me tango x mai i ngā taha e rua o te whārite.
-2\left(-x+2\right)+x=14
Whakakapia te -x+2 mō te y ki tērā atu whārite, -2y+x=14.
2x-4+x=14
Whakareatia -2 ki te -x+2.
3x-4=14
Tāpiri 2x ki te x.
3x=18
Me tāpiri 4 ki ngā taha e rua o te whārite.
x=6
Whakawehea ngā taha e rua ki te 3.
y=-6+2
Whakaurua te 6 mō x ki y=-x+2. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
y=-4
Tāpiri 2 ki te -6.
y=-4,x=6
Kua oti te pūnaha te whakatau.
y+x=2
Whakaarohia te whārite tuatahi. Me tāpiri te x ki ngā taha e rua.
y+x=2,-2y+x=14
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\\-2&1\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}2\\14\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}1&1\\-2&1\end{matrix}\right))\left(\begin{matrix}1&1\\-2&1\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\-2&1\end{matrix}\right))\left(\begin{matrix}2\\14\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&1\\-2&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&1\\-2&1\end{matrix}\right))\left(\begin{matrix}2\\14\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\\-2&1\end{matrix}\right))\left(\begin{matrix}2\\14\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{1}{1-\left(-2\right)}\\-\frac{-2}{1-\left(-2\right)}&\frac{1}{1-\left(-2\right)}\end{matrix}\right)\left(\begin{matrix}2\\14\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{1}{3}\\\frac{2}{3}&\frac{1}{3}\end{matrix}\right)\left(\begin{matrix}2\\14\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{1}{3}\times 2-\frac{1}{3}\times 14\\\frac{2}{3}\times 2+\frac{1}{3}\times 14\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-4\\6\end{matrix}\right)
Mahia ngā tātaitanga.
y=-4,x=6
Tangohia ngā huānga poukapa y me x.
y+x=2
Whakaarohia te whārite tuatahi. Me tāpiri te x ki ngā taha e rua.
y+x=2,-2y+x=14
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+2y+x-x=2-14
Me tango -2y+x=14 mai i y+x=2 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
y+2y=2-14
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=2-14
Tāpiri y ki te 2y.
3y=-12
Tāpiri 2 ki te -14.
y=-4
Whakawehea ngā taha e rua ki te 3.
-2\left(-4\right)+x=14
Whakaurua te -4 mō y ki -2y+x=14. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
8+x=14
Whakareatia -2 ki te -4.
x=6
Me tango 8 mai i ngā taha e rua o te whārite.
y=-4,x=6
Kua oti te pūnaha te whakatau.
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