\left\{ \begin{array} { l } { x = \frac { 3 } { 4 } y } \\ { y = \frac { 8 } { 9 } x - 4 } \end{array} \right.
Whakaoti mō x, y
x=-9
y=-12
Graph
Tohaina
Kua tāruatia ki te papatopenga
x-\frac{3}{4}y=0
Whakaarohia te whārite tuatahi. Tangohia te \frac{3}{4}y mai i ngā taha e rua.
y-\frac{8}{9}x=-4
Whakaarohia te whārite tuarua. Tangohia te \frac{8}{9}x mai i ngā taha e rua.
x-\frac{3}{4}y=0,-\frac{8}{9}x+y=-4
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-\frac{3}{4}y=0
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=\frac{3}{4}y
Me tāpiri \frac{3y}{4} ki ngā taha e rua o te whārite.
-\frac{8}{9}\times \frac{3}{4}y+y=-4
Whakakapia te \frac{3y}{4} mō te x ki tērā atu whārite, -\frac{8}{9}x+y=-4.
-\frac{2}{3}y+y=-4
Whakareatia -\frac{8}{9} ki te \frac{3y}{4}.
\frac{1}{3}y=-4
Tāpiri -\frac{2y}{3} ki te y.
y=-12
Me whakarea ngā taha e rua ki te 3.
x=\frac{3}{4}\left(-12\right)
Whakaurua te -12 mō y ki x=\frac{3}{4}y. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=-9
Whakareatia \frac{3}{4} ki te -12.
x=-9,y=-12
Kua oti te pūnaha te whakatau.
x-\frac{3}{4}y=0
Whakaarohia te whārite tuatahi. Tangohia te \frac{3}{4}y mai i ngā taha e rua.
y-\frac{8}{9}x=-4
Whakaarohia te whārite tuarua. Tangohia te \frac{8}{9}x mai i ngā taha e rua.
x-\frac{3}{4}y=0,-\frac{8}{9}x+y=-4
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}1&-\frac{3}{4}\\-\frac{8}{9}&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}0\\-4\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}1&-\frac{3}{4}\\-\frac{8}{9}&1\end{matrix}\right))\left(\begin{matrix}1&-\frac{3}{4}\\-\frac{8}{9}&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&-\frac{3}{4}\\-\frac{8}{9}&1\end{matrix}\right))\left(\begin{matrix}0\\-4\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&-\frac{3}{4}\\-\frac{8}{9}&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&-\frac{3}{4}\\-\frac{8}{9}&1\end{matrix}\right))\left(\begin{matrix}0\\-4\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&-\frac{3}{4}\\-\frac{8}{9}&1\end{matrix}\right))\left(\begin{matrix}0\\-4\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-\left(-\frac{3}{4}\left(-\frac{8}{9}\right)\right)}&-\frac{-\frac{3}{4}}{1-\left(-\frac{3}{4}\left(-\frac{8}{9}\right)\right)}\\-\frac{-\frac{8}{9}}{1-\left(-\frac{3}{4}\left(-\frac{8}{9}\right)\right)}&\frac{1}{1-\left(-\frac{3}{4}\left(-\frac{8}{9}\right)\right)}\end{matrix}\right)\left(\begin{matrix}0\\-4\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}3&\frac{9}{4}\\\frac{8}{3}&3\end{matrix}\right)\left(\begin{matrix}0\\-4\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{9}{4}\left(-4\right)\\3\left(-4\right)\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-9\\-12\end{matrix}\right)
Mahia ngā tātaitanga.
x=-9,y=-12
Tangohia ngā huānga poukapa x me y.
x-\frac{3}{4}y=0
Whakaarohia te whārite tuatahi. Tangohia te \frac{3}{4}y mai i ngā taha e rua.
y-\frac{8}{9}x=-4
Whakaarohia te whārite tuarua. Tangohia te \frac{8}{9}x mai i ngā taha e rua.
x-\frac{3}{4}y=0,-\frac{8}{9}x+y=-4
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.
-\frac{8}{9}x-\frac{8}{9}\left(-\frac{3}{4}\right)y=0,-\frac{8}{9}x+y=-4
Kia ōrite ai a x me -\frac{8x}{9}, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te -\frac{8}{9} me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 1.
-\frac{8}{9}x+\frac{2}{3}y=0,-\frac{8}{9}x+y=-4
Whakarūnātia.
-\frac{8}{9}x+\frac{8}{9}x+\frac{2}{3}y-y=4
Me tango -\frac{8}{9}x+y=-4 mai i -\frac{8}{9}x+\frac{2}{3}y=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
\frac{2}{3}y-y=4
Tāpiri -\frac{8x}{9} ki te \frac{8x}{9}. Ka whakakore atu ngā kupu -\frac{8x}{9} me \frac{8x}{9}, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
-\frac{1}{3}y=4
Tāpiri \frac{2y}{3} ki te -y.
y=-12
Me whakarea ngā taha e rua ki te -3.
-\frac{8}{9}x-12=-4
Whakaurua te -12 mō y ki -\frac{8}{9}x+y=-4. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
-\frac{8}{9}x=8
Me tāpiri 12 ki ngā taha e rua o te whārite.
x=-9
Whakawehea ngā taha e rua o te whārite ki te -\frac{8}{9}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.
x=-9,y=-12
Kua oti te pūnaha te whakatau.
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