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4x-3y=1,5x+2y=7
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.
4x-3y=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.
4x=3y+1
Me tāpiri 3y ki ngā taha e rua o te whārite.
x=\frac{1}{4}\left(3y+1\right)
Whakawehea ngā taha e rua ki te 4.
x=\frac{3}{4}y+\frac{1}{4}
Whakareatia \frac{1}{4} ki te 3y+1.
5\left(\frac{3}{4}y+\frac{1}{4}\right)+2y=7
Whakakapia te \frac{3y+1}{4} mō te x ki tērā atu whārite, 5x+2y=7.
\frac{15}{4}y+\frac{5}{4}+2y=7
Whakareatia 5 ki te \frac{3y+1}{4}.
\frac{23}{4}y+\frac{5}{4}=7
Tāpiri \frac{15y}{4} ki te 2y.
\frac{23}{4}y=\frac{23}{4}
Me tango \frac{5}{4} mai i ngā taha e rua o te whārite.
y=1
Whakawehea ngā taha e rua o te whārite ki te \frac{23}{4}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.
x=\frac{3+1}{4}
Whakaurua te 1 mō y ki x=\frac{3}{4}y+\frac{1}{4}. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=1
Tāpiri \frac{1}{4} 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=1,y=1
Kua oti te pūnaha te whakatau.
4x-3y=1,5x+2y=7
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}4&-3\\5&2\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}1\\7\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}4&-3\\5&2\end{matrix}\right))\left(\begin{matrix}4&-3\\5&2\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}4&-3\\5&2\end{matrix}\right))\left(\begin{matrix}1\\7\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}4&-3\\5&2\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}4&-3\\5&2\end{matrix}\right))\left(\begin{matrix}1\\7\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}4&-3\\5&2\end{matrix}\right))\left(\begin{matrix}1\\7\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{2}{4\times 2-\left(-3\times 5\right)}&-\frac{-3}{4\times 2-\left(-3\times 5\right)}\\-\frac{5}{4\times 2-\left(-3\times 5\right)}&\frac{4}{4\times 2-\left(-3\times 5\right)}\end{matrix}\right)\left(\begin{matrix}1\\7\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}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{2}{23}&\frac{3}{23}\\-\frac{5}{23}&\frac{4}{23}\end{matrix}\right)\left(\begin{matrix}1\\7\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{2}{23}+\frac{3}{23}\times 7\\-\frac{5}{23}+\frac{4}{23}\times 7\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}1\\1\end{matrix}\right)
Mahia ngā tātaitanga.
x=1,y=1
Tangohia ngā huānga poukapa x me y.
4x-3y=1,5x+2y=7
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.
5\times 4x+5\left(-3\right)y=5,4\times 5x+4\times 2y=4\times 7
Kia ōrite ai a 4x me 5x, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te 5 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 4.
20x-15y=5,20x+8y=28
Whakarūnātia.
20x-20x-15y-8y=5-28
Me tango 20x+8y=28 mai i 20x-15y=5 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
-15y-8y=5-28
Tāpiri 20x ki te -20x. Ka whakakore atu ngā kupu 20x me -20x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
-23y=5-28
Tāpiri -15y ki te -8y.
-23y=-23
Tāpiri 5 ki te -28.
y=1
Whakawehea ngā taha e rua ki te -23.
5x+2=7
Whakaurua te 1 mō y ki 5x+2y=7. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
5x=5
Me tango 2 mai i ngā taha e rua o te whārite.
x=1
Whakawehea ngā taha e rua ki te 5.
x=1,y=1
Kua oti te pūnaha te whakatau.