Whakaoti mō x, y
x=5
y=17
Graph
Tohaina
Kua tāruatia ki te papatopenga
3\left(x+1\right)=y+1
Whakaarohia te whārite tuatahi. Tē taea kia ōrite te tāupe y ki -1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(y+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o y+1,3.
3x+3=y+1
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x+1.
3x+3-y=1
Tangohia te y mai i ngā taha e rua.
3x-y=1-3
Tangohia te 3 mai i ngā taha e rua.
3x-y=-2
Tangohia te 3 i te 1, ka -2.
4\left(x-1\right)=y-1
Whakaarohia te whārite tuarua. Tē taea kia ōrite te tāupe y ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 4\left(y-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o y-1,4.
4x-4=y-1
Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x-1.
4x-4-y=-1
Tangohia te y mai i ngā taha e rua.
4x-y=-1+4
Me tāpiri te 4 ki ngā taha e rua.
4x-y=3
Tāpirihia te -1 ki te 4, ka 3.
3x-y=-2,4x-y=3
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-y=-2
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=y-2
Me tāpiri y ki ngā taha e rua o te whārite.
x=\frac{1}{3}\left(y-2\right)
Whakawehea ngā taha e rua ki te 3.
x=\frac{1}{3}y-\frac{2}{3}
Whakareatia \frac{1}{3} ki te y-2.
4\left(\frac{1}{3}y-\frac{2}{3}\right)-y=3
Whakakapia te \frac{-2+y}{3} mō te x ki tērā atu whārite, 4x-y=3.
\frac{4}{3}y-\frac{8}{3}-y=3
Whakareatia 4 ki te \frac{-2+y}{3}.
\frac{1}{3}y-\frac{8}{3}=3
Tāpiri \frac{4y}{3} ki te -y.
\frac{1}{3}y=\frac{17}{3}
Me tāpiri \frac{8}{3} ki ngā taha e rua o te whārite.
y=17
Me whakarea ngā taha e rua ki te 3.
x=\frac{1}{3}\times 17-\frac{2}{3}
Whakaurua te 17 mō y ki x=\frac{1}{3}y-\frac{2}{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{17-2}{3}
Whakareatia \frac{1}{3} ki te 17.
x=5
Tāpiri -\frac{2}{3} ki te \frac{17}{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=5,y=17
Kua oti te pūnaha te whakatau.
3\left(x+1\right)=y+1
Whakaarohia te whārite tuatahi. Tē taea kia ōrite te tāupe y ki -1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(y+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o y+1,3.
3x+3=y+1
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x+1.
3x+3-y=1
Tangohia te y mai i ngā taha e rua.
3x-y=1-3
Tangohia te 3 mai i ngā taha e rua.
3x-y=-2
Tangohia te 3 i te 1, ka -2.
4\left(x-1\right)=y-1
Whakaarohia te whārite tuarua. Tē taea kia ōrite te tāupe y ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 4\left(y-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o y-1,4.
4x-4=y-1
Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x-1.
4x-4-y=-1
Tangohia te y mai i ngā taha e rua.
4x-y=-1+4
Me tāpiri te 4 ki ngā taha e rua.
4x-y=3
Tāpirihia te -1 ki te 4, ka 3.
3x-y=-2,4x-y=3
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}3&-1\\4&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-2\\3\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}3&-1\\4&-1\end{matrix}\right))\left(\begin{matrix}3&-1\\4&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}3&-1\\4&-1\end{matrix}\right))\left(\begin{matrix}-2\\3\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}3&-1\\4&-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&-1\\4&-1\end{matrix}\right))\left(\begin{matrix}-2\\3\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&-1\\4&-1\end{matrix}\right))\left(\begin{matrix}-2\\3\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\left(-1\right)-\left(-4\right)}&-\frac{-1}{3\left(-1\right)-\left(-4\right)}\\-\frac{4}{3\left(-1\right)-\left(-4\right)}&\frac{3}{3\left(-1\right)-\left(-4\right)}\end{matrix}\right)\left(\begin{matrix}-2\\3\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&1\\-4&3\end{matrix}\right)\left(\begin{matrix}-2\\3\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\left(-2\right)+3\\-4\left(-2\right)+3\times 3\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}5\\17\end{matrix}\right)
Mahia ngā tātaitanga.
x=5,y=17
Tangohia ngā huānga poukapa x me y.
3\left(x+1\right)=y+1
Whakaarohia te whārite tuatahi. Tē taea kia ōrite te tāupe y ki -1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(y+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o y+1,3.
3x+3=y+1
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x+1.
3x+3-y=1
Tangohia te y mai i ngā taha e rua.
3x-y=1-3
Tangohia te 3 mai i ngā taha e rua.
3x-y=-2
Tangohia te 3 i te 1, ka -2.
4\left(x-1\right)=y-1
Whakaarohia te whārite tuarua. Tē taea kia ōrite te tāupe y ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 4\left(y-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o y-1,4.
4x-4=y-1
Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x-1.
4x-4-y=-1
Tangohia te y mai i ngā taha e rua.
4x-y=-1+4
Me tāpiri te 4 ki ngā taha e rua.
4x-y=3
Tāpirihia te -1 ki te 4, ka 3.
3x-y=-2,4x-y=3
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-4x-y+y=-2-3
Me tango 4x-y=3 mai i 3x-y=-2 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
3x-4x=-2-3
Tāpiri -y ki te y. Ka whakakore atu ngā kupu -y me y, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
-x=-2-3
Tāpiri 3x ki te -4x.
-x=-5
Tāpiri -2 ki te -3.
x=5
Whakawehea ngā taha e rua ki te -1.
4\times 5-y=3
Whakaurua te 5 mō x ki 4x-y=3. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
20-y=3
Whakareatia 4 ki te 5.
-y=-17
Me tango 20 mai i ngā taha e rua o te whārite.
y=17
Whakawehea ngā taha e rua ki te -1.
x=5,y=17
Kua oti te pūnaha te whakatau.
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