\left\{ \begin{array} { l } { \frac { 3 x - 1 } { 2 } - \frac { 4 y - 7 } { 3 } = 2 } \\ { \frac { 3 y - 6 } { 4 } - \frac { 5 - x } { 6 } = - 1 \frac { 5 } { 12 } } \end{array} \right.
Whakaoti mō x, y
x=1
y=1
Graph
Tohaina
Kua tāruatia ki te papatopenga
3\left(3x-1\right)-2\left(4y-7\right)=12
Whakaarohia te whārite tuatahi. Me whakarea ngā taha e rua o te whārite ki te 6, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3.
9x-3-2\left(4y-7\right)=12
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 3x-1.
9x-3-8y+14=12
Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te 4y-7.
9x+11-8y=12
Tāpirihia te -3 ki te 14, ka 11.
9x-8y=12-11
Tangohia te 11 mai i ngā taha e rua.
9x-8y=1
Tangohia te 11 i te 12, ka 1.
3\left(3y-6\right)-2\left(5-x\right)=-\left(1\times 12+5\right)
Whakaarohia te whārite tuarua. Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 4,6,12.
9y-18-2\left(5-x\right)=-\left(1\times 12+5\right)
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 3y-6.
9y-18-10+2x=-\left(1\times 12+5\right)
Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te 5-x.
9y-28+2x=-\left(1\times 12+5\right)
Tangohia te 10 i te -18, ka -28.
9y-28+2x=-\left(12+5\right)
Whakareatia te 1 ki te 12, ka 12.
9y-28+2x=-17
Tāpirihia te 12 ki te 5, ka 17.
9y+2x=-17+28
Me tāpiri te 28 ki ngā taha e rua.
9y+2x=11
Tāpirihia te -17 ki te 28, ka 11.
9x-8y=1,2x+9y=11
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.
9x-8y=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.
9x=8y+1
Me tāpiri 8y ki ngā taha e rua o te whārite.
x=\frac{1}{9}\left(8y+1\right)
Whakawehea ngā taha e rua ki te 9.
x=\frac{8}{9}y+\frac{1}{9}
Whakareatia \frac{1}{9} ki te 8y+1.
2\left(\frac{8}{9}y+\frac{1}{9}\right)+9y=11
Whakakapia te \frac{8y+1}{9} mō te x ki tērā atu whārite, 2x+9y=11.
\frac{16}{9}y+\frac{2}{9}+9y=11
Whakareatia 2 ki te \frac{8y+1}{9}.
\frac{97}{9}y+\frac{2}{9}=11
Tāpiri \frac{16y}{9} ki te 9y.
\frac{97}{9}y=\frac{97}{9}
Me tango \frac{2}{9} mai i ngā taha e rua o te whārite.
y=1
Whakawehea ngā taha e rua o te whārite ki te \frac{97}{9}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.
x=\frac{8+1}{9}
Whakaurua te 1 mō y ki x=\frac{8}{9}y+\frac{1}{9}. 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}{9} ki te \frac{8}{9} 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.
3\left(3x-1\right)-2\left(4y-7\right)=12
Whakaarohia te whārite tuatahi. Me whakarea ngā taha e rua o te whārite ki te 6, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3.
9x-3-2\left(4y-7\right)=12
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 3x-1.
9x-3-8y+14=12
Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te 4y-7.
9x+11-8y=12
Tāpirihia te -3 ki te 14, ka 11.
9x-8y=12-11
Tangohia te 11 mai i ngā taha e rua.
9x-8y=1
Tangohia te 11 i te 12, ka 1.
3\left(3y-6\right)-2\left(5-x\right)=-\left(1\times 12+5\right)
Whakaarohia te whārite tuarua. Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 4,6,12.
9y-18-2\left(5-x\right)=-\left(1\times 12+5\right)
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 3y-6.
9y-18-10+2x=-\left(1\times 12+5\right)
Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te 5-x.
9y-28+2x=-\left(1\times 12+5\right)
Tangohia te 10 i te -18, ka -28.
9y-28+2x=-\left(12+5\right)
Whakareatia te 1 ki te 12, ka 12.
9y-28+2x=-17
Tāpirihia te 12 ki te 5, ka 17.
9y+2x=-17+28
Me tāpiri te 28 ki ngā taha e rua.
9y+2x=11
Tāpirihia te -17 ki te 28, ka 11.
9x-8y=1,2x+9y=11
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}9&-8\\2&9\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}1\\11\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}9&-8\\2&9\end{matrix}\right))\left(\begin{matrix}9&-8\\2&9\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}9&-8\\2&9\end{matrix}\right))\left(\begin{matrix}1\\11\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}9&-8\\2&9\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}9&-8\\2&9\end{matrix}\right))\left(\begin{matrix}1\\11\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}9&-8\\2&9\end{matrix}\right))\left(\begin{matrix}1\\11\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{9}{9\times 9-\left(-8\times 2\right)}&-\frac{-8}{9\times 9-\left(-8\times 2\right)}\\-\frac{2}{9\times 9-\left(-8\times 2\right)}&\frac{9}{9\times 9-\left(-8\times 2\right)}\end{matrix}\right)\left(\begin{matrix}1\\11\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{9}{97}&\frac{8}{97}\\-\frac{2}{97}&\frac{9}{97}\end{matrix}\right)\left(\begin{matrix}1\\11\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{9}{97}+\frac{8}{97}\times 11\\-\frac{2}{97}+\frac{9}{97}\times 11\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.
3\left(3x-1\right)-2\left(4y-7\right)=12
Whakaarohia te whārite tuatahi. Me whakarea ngā taha e rua o te whārite ki te 6, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3.
9x-3-2\left(4y-7\right)=12
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 3x-1.
9x-3-8y+14=12
Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te 4y-7.
9x+11-8y=12
Tāpirihia te -3 ki te 14, ka 11.
9x-8y=12-11
Tangohia te 11 mai i ngā taha e rua.
9x-8y=1
Tangohia te 11 i te 12, ka 1.
3\left(3y-6\right)-2\left(5-x\right)=-\left(1\times 12+5\right)
Whakaarohia te whārite tuarua. Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 4,6,12.
9y-18-2\left(5-x\right)=-\left(1\times 12+5\right)
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 3y-6.
9y-18-10+2x=-\left(1\times 12+5\right)
Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te 5-x.
9y-28+2x=-\left(1\times 12+5\right)
Tangohia te 10 i te -18, ka -28.
9y-28+2x=-\left(12+5\right)
Whakareatia te 1 ki te 12, ka 12.
9y-28+2x=-17
Tāpirihia te 12 ki te 5, ka 17.
9y+2x=-17+28
Me tāpiri te 28 ki ngā taha e rua.
9y+2x=11
Tāpirihia te -17 ki te 28, ka 11.
9x-8y=1,2x+9y=11
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.
2\times 9x+2\left(-8\right)y=2,9\times 2x+9\times 9y=9\times 11
Kia ōrite ai a 9x me 2x, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te 2 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 9.
18x-16y=2,18x+81y=99
Whakarūnātia.
18x-18x-16y-81y=2-99
Me tango 18x+81y=99 mai i 18x-16y=2 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
-16y-81y=2-99
Tāpiri 18x ki te -18x. Ka whakakore atu ngā kupu 18x me -18x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
-97y=2-99
Tāpiri -16y ki te -81y.
-97y=-97
Tāpiri 2 ki te -99.
y=1
Whakawehea ngā taha e rua ki te -97.
2x+9=11
Whakaurua te 1 mō y ki 2x+9y=11. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
2x=2
Me tango 9 mai i ngā taha e rua o te whārite.
x=1
Whakawehea ngā taha e rua ki te 2.
x=1,y=1
Kua oti te pūnaha te whakatau.
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