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y-\frac{1}{4}x=3
Whakaarohia te whārite tuarua. Tangohia te \frac{1}{4}x mai i ngā taha e rua.
2x+y=-6,-\frac{1}{4}x+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.
2x+y=-6
Kōwhiria tētahi o ngā whārite ka whakaotia mō te x mā te wehe i te x i te taha mauī o te tohu ōrite.
2x=-y-6
Me tango y mai i ngā taha e rua o te whārite.
x=\frac{1}{2}\left(-y-6\right)
Whakawehea ngā taha e rua ki te 2.
x=-\frac{1}{2}y-3
Whakareatia \frac{1}{2} ki te -y-6.
-\frac{1}{4}\left(-\frac{1}{2}y-3\right)+y=3
Whakakapia te -\frac{y}{2}-3 mō te x ki tērā atu whārite, -\frac{1}{4}x+y=3.
\frac{1}{8}y+\frac{3}{4}+y=3
Whakareatia -\frac{1}{4} ki te -\frac{y}{2}-3.
\frac{9}{8}y+\frac{3}{4}=3
Tāpiri \frac{y}{8} ki te y.
\frac{9}{8}y=\frac{9}{4}
Me tango \frac{3}{4} mai i ngā taha e rua o te whārite.
y=2
Whakawehea ngā taha e rua o te whārite ki te \frac{9}{8}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.
x=-\frac{1}{2}\times 2-3
Whakaurua te 2 mō y ki x=-\frac{1}{2}y-3. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=-1-3
Whakareatia -\frac{1}{2} ki te 2.
x=-4
Tāpiri -3 ki te -1.
x=-4,y=2
Kua oti te pūnaha te whakatau.
y-\frac{1}{4}x=3
Whakaarohia te whārite tuarua. Tangohia te \frac{1}{4}x mai i ngā taha e rua.
2x+y=-6,-\frac{1}{4}x+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}2&1\\-\frac{1}{4}&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-6\\3\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}2&1\\-\frac{1}{4}&1\end{matrix}\right))\left(\begin{matrix}2&1\\-\frac{1}{4}&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&1\\-\frac{1}{4}&1\end{matrix}\right))\left(\begin{matrix}-6\\3\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}2&1\\-\frac{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}2&1\\-\frac{1}{4}&1\end{matrix}\right))\left(\begin{matrix}-6\\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}2&1\\-\frac{1}{4}&1\end{matrix}\right))\left(\begin{matrix}-6\\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}{2-\left(-\frac{1}{4}\right)}&-\frac{1}{2-\left(-\frac{1}{4}\right)}\\-\frac{-\frac{1}{4}}{2-\left(-\frac{1}{4}\right)}&\frac{2}{2-\left(-\frac{1}{4}\right)}\end{matrix}\right)\left(\begin{matrix}-6\\3\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{4}{9}&-\frac{4}{9}\\\frac{1}{9}&\frac{8}{9}\end{matrix}\right)\left(\begin{matrix}-6\\3\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{4}{9}\left(-6\right)-\frac{4}{9}\times 3\\\frac{1}{9}\left(-6\right)+\frac{8}{9}\times 3\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-4\\2\end{matrix}\right)
Mahia ngā tātaitanga.
x=-4,y=2
Tangohia ngā huānga poukapa x me y.
y-\frac{1}{4}x=3
Whakaarohia te whārite tuarua. Tangohia te \frac{1}{4}x mai i ngā taha e rua.
2x+y=-6,-\frac{1}{4}x+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.
2x+\frac{1}{4}x+y-y=-6-3
Me tango -\frac{1}{4}x+y=3 mai i 2x+y=-6 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
2x+\frac{1}{4}x=-6-3
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.
\frac{9}{4}x=-6-3
Tāpiri 2x ki te \frac{x}{4}.
\frac{9}{4}x=-9
Tāpiri -6 ki te -3.
x=-4
Whakawehea ngā taha e rua o te whārite ki te \frac{9}{4}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.
-\frac{1}{4}\left(-4\right)+y=3
Whakaurua te -4 mō x ki -\frac{1}{4}x+y=3. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
1+y=3
Whakareatia -\frac{1}{4} ki te -4.
y=2
Me tango 1 mai i ngā taha e rua o te whārite.
x=-4,y=2
Kua oti te pūnaha te whakatau.