Whakaoti mō x, y
x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667
y = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333
Graph
Tohaina
Kua tāruatia ki te papatopenga
2x-y=1,x+y=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-y=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=y+1
Me tāpiri y ki ngā taha e rua o te whārite.
x=\frac{1}{2}\left(y+1\right)
Whakawehea ngā taha e rua ki te 2.
x=\frac{1}{2}y+\frac{1}{2}
Whakareatia \frac{1}{2} ki te y+1.
\frac{1}{2}y+\frac{1}{2}+y=4
Whakakapia te \frac{1+y}{2} mō te x ki tērā atu whārite, x+y=4.
\frac{3}{2}y+\frac{1}{2}=4
Tāpiri \frac{y}{2} ki te y.
\frac{3}{2}y=\frac{7}{2}
Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.
y=\frac{7}{3}
Whakawehea ngā taha e rua o te whārite ki te \frac{3}{2}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.
x=\frac{1}{2}\times \frac{7}{3}+\frac{1}{2}
Whakaurua te \frac{7}{3} mō y ki x=\frac{1}{2}y+\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=\frac{7}{6}+\frac{1}{2}
Whakareatia \frac{1}{2} ki te \frac{7}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
x=\frac{5}{3}
Tāpiri \frac{1}{2} ki te \frac{7}{6} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
x=\frac{5}{3},y=\frac{7}{3}
Kua oti te pūnaha te whakatau.
2x-y=1,x+y=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&-1\\1&1\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&-1\\1&1\end{matrix}\right))\left(\begin{matrix}2&-1\\1&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&-1\\1&1\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&-1\\1&1\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&-1\\1&1\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&-1\\1&1\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{1}{2-\left(-1\right)}&-\frac{-1}{2-\left(-1\right)}\\-\frac{1}{2-\left(-1\right)}&\frac{2}{2-\left(-1\right)}\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{1}{3}&\frac{1}{3}\\-\frac{1}{3}&\frac{2}{3}\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{1}{3}+\frac{1}{3}\times 4\\-\frac{1}{3}+\frac{2}{3}\times 4\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{5}{3}\\\frac{7}{3}\end{matrix}\right)
Mahia ngā tātaitanga.
x=\frac{5}{3},y=\frac{7}{3}
Tangohia ngā huānga poukapa x me y.
2x-y=1,x+y=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-y=1,2x+2y=2\times 4
Kia ōrite ai a 2x me x, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te 1 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 2.
2x-y=1,2x+2y=8
Whakarūnātia.
2x-2x-y-2y=1-8
Me tango 2x+2y=8 mai i 2x-y=1 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
-y-2y=1-8
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.
-3y=1-8
Tāpiri -y ki te -2y.
-3y=-7
Tāpiri 1 ki te -8.
y=\frac{7}{3}
Whakawehea ngā taha e rua ki te -3.
x+\frac{7}{3}=4
Whakaurua te \frac{7}{3} mō y ki x+y=4. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=\frac{5}{3}
Me tango \frac{7}{3} mai i ngā taha e rua o te whārite.
x=\frac{5}{3},y=\frac{7}{3}
Kua oti te pūnaha te whakatau.
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