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2x+3y=5,2x-y=3
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+3y=5
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=-3y+5
Me tango 3y mai i ngā taha e rua o te whārite.
x=\frac{1}{2}\left(-3y+5\right)
Whakawehea ngā taha e rua ki te 2.
x=-\frac{3}{2}y+\frac{5}{2}
Whakareatia \frac{1}{2} ki te -3y+5.
2\left(-\frac{3}{2}y+\frac{5}{2}\right)-y=3
Whakakapia te \frac{-3y+5}{2} mō te x ki tērā atu whārite, 2x-y=3.
-3y+5-y=3
Whakareatia 2 ki te \frac{-3y+5}{2}.
-4y+5=3
Tāpiri -3y ki te -y.
-4y=-2
Me tango 5 mai i ngā taha e rua o te whārite.
y=\frac{1}{2}
Whakawehea ngā taha e rua ki te -4.
x=-\frac{3}{2}\times \frac{1}{2}+\frac{5}{2}
Whakaurua te \frac{1}{2} mō y ki x=-\frac{3}{2}y+\frac{5}{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{3}{4}+\frac{5}{2}
Whakareatia -\frac{3}{2} ki te \frac{1}{2} 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{7}{4}
Tāpiri \frac{5}{2} ki te -\frac{3}{4} 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{7}{4},y=\frac{1}{2}
Kua oti te pūnaha te whakatau.
2x+3y=5,2x-y=3
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}2&3\\2&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}5\\3\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}2&3\\2&-1\end{matrix}\right))\left(\begin{matrix}2&3\\2&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&3\\2&-1\end{matrix}\right))\left(\begin{matrix}5\\3\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}2&3\\2&-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&3\\2&-1\end{matrix}\right))\left(\begin{matrix}5\\3\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&3\\2&-1\end{matrix}\right))\left(\begin{matrix}5\\3\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)-3\times 2}&-\frac{3}{2\left(-1\right)-3\times 2}\\-\frac{2}{2\left(-1\right)-3\times 2}&\frac{2}{2\left(-1\right)-3\times 2}\end{matrix}\right)\left(\begin{matrix}5\\3\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}{8}&\frac{3}{8}\\\frac{1}{4}&-\frac{1}{4}\end{matrix}\right)\left(\begin{matrix}5\\3\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{8}\times 5+\frac{3}{8}\times 3\\\frac{1}{4}\times 5-\frac{1}{4}\times 3\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{7}{4}\\\frac{1}{2}\end{matrix}\right)
Mahia ngā tātaitanga.
x=\frac{7}{4},y=\frac{1}{2}
Tangohia ngā huānga poukapa x me y.
2x+3y=5,2x-y=3
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+3y+y=5-3
Me tango 2x-y=3 mai i 2x+3y=5 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
3y+y=5-3
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.
4y=5-3
Tāpiri 3y ki te y.
4y=2
Tāpiri 5 ki te -3.
y=\frac{1}{2}
Whakawehea ngā taha e rua ki te 4.
2x-\frac{1}{2}=3
Whakaurua te \frac{1}{2} mō y ki 2x-y=3. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
2x=\frac{7}{2}
Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.
x=\frac{7}{4}
Whakawehea ngā taha e rua ki te 2.
x=\frac{7}{4},y=\frac{1}{2}
Kua oti te pūnaha te whakatau.