Whakaoti mō y, x
x=-1
y=4
Graph
Tohaina
Kua tāruatia ki te papatopenga
y-x=5
Whakaarohia te whārite tuatahi. Tangohia te x mai i ngā taha e rua.
y+4x=0
Whakaarohia te whārite tuarua. Me tāpiri te 4x ki ngā taha e rua.
y-x=5,y+4x=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.
y-x=5
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+5
Me tāpiri x ki ngā taha e rua o te whārite.
x+5+4x=0
Whakakapia te x+5 mō te y ki tērā atu whārite, y+4x=0.
5x+5=0
Tāpiri x ki te 4x.
5x=-5
Me tango 5 mai i ngā taha e rua o te whārite.
x=-1
Whakawehea ngā taha e rua ki te 5.
y=-1+5
Whakaurua te -1 mō x ki y=x+5. 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 5 ki te -1.
y=4,x=-1
Kua oti te pūnaha te whakatau.
y-x=5
Whakaarohia te whārite tuatahi. Tangohia te x mai i ngā taha e rua.
y+4x=0
Whakaarohia te whārite tuarua. Me tāpiri te 4x ki ngā taha e rua.
y-x=5,y+4x=0
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&4\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}5\\0\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}1&-1\\1&4\end{matrix}\right))\left(\begin{matrix}1&-1\\1&4\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-1\\1&4\end{matrix}\right))\left(\begin{matrix}5\\0\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&-1\\1&4\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&4\end{matrix}\right))\left(\begin{matrix}5\\0\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&4\end{matrix}\right))\left(\begin{matrix}5\\0\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{4}{4-\left(-1\right)}&-\frac{-1}{4-\left(-1\right)}\\-\frac{1}{4-\left(-1\right)}&\frac{1}{4-\left(-1\right)}\end{matrix}\right)\left(\begin{matrix}5\\0\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{4}{5}&\frac{1}{5}\\-\frac{1}{5}&\frac{1}{5}\end{matrix}\right)\left(\begin{matrix}5\\0\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{4}{5}\times 5\\-\frac{1}{5}\times 5\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}4\\-1\end{matrix}\right)
Mahia ngā tātaitanga.
y=4,x=-1
Tangohia ngā huānga poukapa y me x.
y-x=5
Whakaarohia te whārite tuatahi. Tangohia te x mai i ngā taha e rua.
y+4x=0
Whakaarohia te whārite tuarua. Me tāpiri te 4x ki ngā taha e rua.
y-x=5,y+4x=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.
y-y-x-4x=5
Me tango y+4x=0 mai i y-x=5 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
-x-4x=5
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.
-5x=5
Tāpiri -x ki te -4x.
x=-1
Whakawehea ngā taha e rua ki te -5.
y+4\left(-1\right)=0
Whakaurua te -1 mō x ki y+4x=0. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
y-4=0
Whakareatia 4 ki te -1.
y=4
Me tāpiri 4 ki ngā taha e rua o te whārite.
y=4,x=-1
Kua oti te pūnaha te whakatau.
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