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