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Whakaoti mō x, y
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4x+6y=-3,5x+7y=-2
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+6y=-3
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=-6y-3
Me tango 6y mai i ngā taha e rua o te whārite.
x=\frac{1}{4}\left(-6y-3\right)
Whakawehea ngā taha e rua ki te 4.
x=-\frac{3}{2}y-\frac{3}{4}
Whakareatia \frac{1}{4} ki te -6y-3.
5\left(-\frac{3}{2}y-\frac{3}{4}\right)+7y=-2
Whakakapia te -\frac{3y}{2}-\frac{3}{4} mō te x ki tērā atu whārite, 5x+7y=-2.
-\frac{15}{2}y-\frac{15}{4}+7y=-2
Whakareatia 5 ki te -\frac{3y}{2}-\frac{3}{4}.
-\frac{1}{2}y-\frac{15}{4}=-2
Tāpiri -\frac{15y}{2} ki te 7y.
-\frac{1}{2}y=\frac{7}{4}
Me tāpiri \frac{15}{4} ki ngā taha e rua o te whārite.
y=-\frac{7}{2}
Me whakarea ngā taha e rua ki te -2.
x=-\frac{3}{2}\left(-\frac{7}{2}\right)-\frac{3}{4}
Whakaurua te -\frac{7}{2} mō y ki x=-\frac{3}{2}y-\frac{3}{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{21-3}{4}
Whakareatia -\frac{3}{2} ki te -\frac{7}{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{9}{2}
Tāpiri -\frac{3}{4} ki te \frac{21}{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{9}{2},y=-\frac{7}{2}
Kua oti te pūnaha te whakatau.
4x+6y=-3,5x+7y=-2
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}4&6\\5&7\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-3\\-2\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}4&6\\5&7\end{matrix}\right))\left(\begin{matrix}4&6\\5&7\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}4&6\\5&7\end{matrix}\right))\left(\begin{matrix}-3\\-2\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}4&6\\5&7\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&6\\5&7\end{matrix}\right))\left(\begin{matrix}-3\\-2\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&6\\5&7\end{matrix}\right))\left(\begin{matrix}-3\\-2\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{7}{4\times 7-6\times 5}&-\frac{6}{4\times 7-6\times 5}\\-\frac{5}{4\times 7-6\times 5}&\frac{4}{4\times 7-6\times 5}\end{matrix}\right)\left(\begin{matrix}-3\\-2\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{7}{2}&3\\\frac{5}{2}&-2\end{matrix}\right)\left(\begin{matrix}-3\\-2\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{7}{2}\left(-3\right)+3\left(-2\right)\\\frac{5}{2}\left(-3\right)-2\left(-2\right)\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{9}{2}\\-\frac{7}{2}\end{matrix}\right)
Mahia ngā tātaitanga.
x=\frac{9}{2},y=-\frac{7}{2}
Tangohia ngā huānga poukapa x me y.
4x+6y=-3,5x+7y=-2
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\times 6y=5\left(-3\right),4\times 5x+4\times 7y=4\left(-2\right)
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+30y=-15,20x+28y=-8
Whakarūnātia.
20x-20x+30y-28y=-15+8
Me tango 20x+28y=-8 mai i 20x+30y=-15 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
30y-28y=-15+8
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.
2y=-15+8
Tāpiri 30y ki te -28y.
2y=-7
Tāpiri -15 ki te 8.
y=-\frac{7}{2}
Whakawehea ngā taha e rua ki te 2.
5x+7\left(-\frac{7}{2}\right)=-2
Whakaurua te -\frac{7}{2} mō y ki 5x+7y=-2. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
5x-\frac{49}{2}=-2
Whakareatia 7 ki te -\frac{7}{2}.
5x=\frac{45}{2}
Me tāpiri \frac{49}{2} ki ngā taha e rua o te whārite.
x=\frac{9}{2}
Whakawehea ngā taha e rua ki te 5.
x=\frac{9}{2},y=-\frac{7}{2}
Kua oti te pūnaha te whakatau.