Whakaoti mō x, y
x = \frac{81}{2} = 40\frac{1}{2} = 40.5
y = \frac{39}{2} = 19\frac{1}{2} = 19.5
Graph
Tohaina
Kua tāruatia ki te papatopenga
x+y=60,x-y=21
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.
x+y=60
Kōwhiria tētahi o ngā whārite ka whakaotia mō te x mā te wehe i te x i te taha mauī o te tohu ōrite.
x=-y+60
Me tango y mai i ngā taha e rua o te whārite.
-y+60-y=21
Whakakapia te -y+60 mō te x ki tērā atu whārite, x-y=21.
-2y+60=21
Tāpiri -y ki te -y.
-2y=-39
Me tango 60 mai i ngā taha e rua o te whārite.
y=\frac{39}{2}
Whakawehea ngā taha e rua ki te -2.
x=-\frac{39}{2}+60
Whakaurua te \frac{39}{2} mō y ki x=-y+60. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=\frac{81}{2}
Tāpiri 60 ki te -\frac{39}{2}.
x=\frac{81}{2},y=\frac{39}{2}
Kua oti te pūnaha te whakatau.
x+y=60,x-y=21
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}1&1\\1&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}60\\21\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}1&1\\1&-1\end{matrix}\right))\left(\begin{matrix}1&1\\1&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\1&-1\end{matrix}\right))\left(\begin{matrix}60\\21\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&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}1&1\\1&-1\end{matrix}\right))\left(\begin{matrix}60\\21\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}1&1\\1&-1\end{matrix}\right))\left(\begin{matrix}60\\21\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}{-1-1}&-\frac{1}{-1-1}\\-\frac{1}{-1-1}&\frac{1}{-1-1}\end{matrix}\right)\left(\begin{matrix}60\\21\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}{2}&\frac{1}{2}\\\frac{1}{2}&-\frac{1}{2}\end{matrix}\right)\left(\begin{matrix}60\\21\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{2}\times 60+\frac{1}{2}\times 21\\\frac{1}{2}\times 60-\frac{1}{2}\times 21\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{81}{2}\\\frac{39}{2}\end{matrix}\right)
Mahia ngā tātaitanga.
x=\frac{81}{2},y=\frac{39}{2}
Tangohia ngā huānga poukapa x me y.
x+y=60,x-y=21
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.
x-x+y+y=60-21
Me tango x-y=21 mai i x+y=60 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
y+y=60-21
Tāpiri x ki te -x. Ka whakakore atu ngā kupu x me -x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
2y=60-21
Tāpiri y ki te y.
2y=39
Tāpiri 60 ki te -21.
y=\frac{39}{2}
Whakawehea ngā taha e rua ki te 2.
x-\frac{39}{2}=21
Whakaurua te \frac{39}{2} mō y ki x-y=21. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=\frac{81}{2}
Me tāpiri \frac{39}{2} ki ngā taha e rua o te whārite.
x=\frac{81}{2},y=\frac{39}{2}
Kua oti te pūnaha te whakatau.
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