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