\left\{ \begin{array} { l } { 2 x + 4 y = 1 } \\ { 2 x - 6 y = - 4 } \end{array} \right.
Whakaoti mō x, y
x=-\frac{1}{2}=-0.5
y=\frac{1}{2}=0.5
Graph
Tohaina
Kua tāruatia ki te papatopenga
2x+4y=1,2x-6y=-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.
2x+4y=1
Kōwhiria tētahi o ngā whārite ka whakaotia mō te x mā te wehe i te x i te taha mauī o te tohu ōrite.
2x=-4y+1
Me tango 4y mai i ngā taha e rua o te whārite.
x=\frac{1}{2}\left(-4y+1\right)
Whakawehea ngā taha e rua ki te 2.
x=-2y+\frac{1}{2}
Whakareatia \frac{1}{2} ki te -4y+1.
2\left(-2y+\frac{1}{2}\right)-6y=-4
Whakakapia te -2y+\frac{1}{2} mō te x ki tērā atu whārite, 2x-6y=-4.
-4y+1-6y=-4
Whakareatia 2 ki te -2y+\frac{1}{2}.
-10y+1=-4
Tāpiri -4y ki te -6y.
-10y=-5
Me tango 1 mai i ngā taha e rua o te whārite.
y=\frac{1}{2}
Whakawehea ngā taha e rua ki te -10.
x=-2\times \frac{1}{2}+\frac{1}{2}
Whakaurua te \frac{1}{2} mō y ki x=-2y+\frac{1}{2}. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=-1+\frac{1}{2}
Whakareatia -2 ki te \frac{1}{2}.
x=-\frac{1}{2}
Tāpiri \frac{1}{2} ki te -1.
x=-\frac{1}{2},y=\frac{1}{2}
Kua oti te pūnaha te whakatau.
2x+4y=1,2x-6y=-4
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}2&4\\2&-6\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}1\\-4\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}2&4\\2&-6\end{matrix}\right))\left(\begin{matrix}2&4\\2&-6\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&4\\2&-6\end{matrix}\right))\left(\begin{matrix}1\\-4\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}2&4\\2&-6\end{matrix}\right).
\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&4\\2&-6\end{matrix}\right))\left(\begin{matrix}1\\-4\end{matrix}\right)
Ko te hua o tētahi poukapa me te kōaro ko te poukapa tuakiri.
\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&4\\2&-6\end{matrix}\right))\left(\begin{matrix}1\\-4\end{matrix}\right)
Whakareatia ngā poukapa kei te taha mauī o te tohu ōrite.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{6}{2\left(-6\right)-4\times 2}&-\frac{4}{2\left(-6\right)-4\times 2}\\-\frac{2}{2\left(-6\right)-4\times 2}&\frac{2}{2\left(-6\right)-4\times 2}\end{matrix}\right)\left(\begin{matrix}1\\-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}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{3}{10}&\frac{1}{5}\\\frac{1}{10}&-\frac{1}{10}\end{matrix}\right)\left(\begin{matrix}1\\-4\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{3}{10}+\frac{1}{5}\left(-4\right)\\\frac{1}{10}-\frac{1}{10}\left(-4\right)\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{2}\\\frac{1}{2}\end{matrix}\right)
Mahia ngā tātaitanga.
x=-\frac{1}{2},y=\frac{1}{2}
Tangohia ngā huānga poukapa x me y.
2x+4y=1,2x-6y=-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.
2x-2x+4y+6y=1+4
Me tango 2x-6y=-4 mai i 2x+4y=1 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
4y+6y=1+4
Tāpiri 2x ki te -2x. Ka whakakore atu ngā kupu 2x me -2x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
10y=1+4
Tāpiri 4y ki te 6y.
10y=5
Tāpiri 1 ki te 4.
y=\frac{1}{2}
Whakawehea ngā taha e rua ki te 10.
2x-6\times \frac{1}{2}=-4
Whakaurua te \frac{1}{2} mō y ki 2x-6y=-4. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
2x-3=-4
Whakareatia -6 ki te \frac{1}{2}.
2x=-1
Me tāpiri 3 ki ngā taha e rua o te whārite.
x=-\frac{1}{2}
Whakawehea ngā taha e rua ki te 2.
x=-\frac{1}{2},y=\frac{1}{2}
Kua oti te pūnaha te whakatau.
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