Whakaoti mō y, x
x=-1
y=-4
Graph
Tohaina
Kua tāruatia ki te papatopenga
y-4x=0
Whakaarohia te whārite tuatahi. Tangohia te 4x mai i ngā taha e rua.
y-3x=-1
Whakaarohia te whārite tuarua. Tangohia te 3x mai i ngā taha e rua.
y-4x=0,y-3x=-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-4x=0
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=4x
Me tāpiri 4x ki ngā taha e rua o te whārite.
4x-3x=-1
Whakakapia te 4x mō te y ki tērā atu whārite, y-3x=-1.
x=-1
Tāpiri 4x ki te -3x.
y=4\left(-1\right)
Whakaurua te -1 mō x ki y=4x. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
y=-4
Whakareatia 4 ki te -1.
y=-4,x=-1
Kua oti te pūnaha te whakatau.
y-4x=0
Whakaarohia te whārite tuatahi. Tangohia te 4x mai i ngā taha e rua.
y-3x=-1
Whakaarohia te whārite tuarua. Tangohia te 3x mai i ngā taha e rua.
y-4x=0,y-3x=-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&-4\\1&-3\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}0\\-1\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}1&-4\\1&-3\end{matrix}\right))\left(\begin{matrix}1&-4\\1&-3\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-4\\1&-3\end{matrix}\right))\left(\begin{matrix}0\\-1\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&-4\\1&-3\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&-4\\1&-3\end{matrix}\right))\left(\begin{matrix}0\\-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&-4\\1&-3\end{matrix}\right))\left(\begin{matrix}0\\-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{3}{-3-\left(-4\right)}&-\frac{-4}{-3-\left(-4\right)}\\-\frac{1}{-3-\left(-4\right)}&\frac{1}{-3-\left(-4\right)}\end{matrix}\right)\left(\begin{matrix}0\\-1\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}-3&4\\-1&1\end{matrix}\right)\left(\begin{matrix}0\\-1\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}4\left(-1\right)\\-1\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-4x=0
Whakaarohia te whārite tuatahi. Tangohia te 4x mai i ngā taha e rua.
y-3x=-1
Whakaarohia te whārite tuarua. Tangohia te 3x mai i ngā taha e rua.
y-4x=0,y-3x=-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-4x+3x=1
Me tango y-3x=-1 mai i y-4x=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
-4x+3x=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.
-x=1
Tāpiri -4x ki te 3x.
x=-1
Whakawehea ngā taha e rua ki te -1.
y-3\left(-1\right)=-1
Whakaurua te -1 mō x ki y-3x=-1. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
y+3=-1
Whakareatia -3 ki te -1.
y=-4
Me tango 3 mai i ngā taha e rua o te whārite.
y=-4,x=-1
Kua oti te pūnaha te whakatau.
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