\left\{ \begin{array} { l } { ( A + B ) \frac { 1 } { 2 } - B = \frac { 3 } { 4 } } \\ { ( 2 A + B ) \frac { 1 } { 4 } - B = \frac { 5 } { 4 } } \end{array} \right.
Whakaoti mō A, B
A=-\frac{1}{2}=-0.5
B=-2
Tohaina
Kua tāruatia ki te papatopenga
\frac{1}{2}A+\frac{1}{2}B-B=\frac{3}{4}
Whakaarohia te whārite tuatahi. Whakamahia te āhuatanga tohatoha hei whakarea te A+B ki te \frac{1}{2}.
\frac{1}{2}A-\frac{1}{2}B=\frac{3}{4}
Pahekotia te \frac{1}{2}B me -B, ka -\frac{1}{2}B.
\frac{1}{2}A+\frac{1}{4}B-B=\frac{5}{4}
Whakaarohia te whārite tuarua. Whakamahia te āhuatanga tohatoha hei whakarea te 2A+B ki te \frac{1}{4}.
\frac{1}{2}A-\frac{3}{4}B=\frac{5}{4}
Pahekotia te \frac{1}{4}B me -B, ka -\frac{3}{4}B.
\frac{1}{2}A-\frac{1}{2}B=\frac{3}{4},\frac{1}{2}A-\frac{3}{4}B=\frac{5}{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.
\frac{1}{2}A-\frac{1}{2}B=\frac{3}{4}
Kōwhiria tētahi o ngā whārite ka whakaotia mō te A mā te wehe i te A i te taha mauī o te tohu ōrite.
\frac{1}{2}A=\frac{1}{2}B+\frac{3}{4}
Me tāpiri \frac{B}{2} ki ngā taha e rua o te whārite.
A=2\left(\frac{1}{2}B+\frac{3}{4}\right)
Me whakarea ngā taha e rua ki te 2.
A=B+\frac{3}{2}
Whakareatia 2 ki te \frac{B}{2}+\frac{3}{4}.
\frac{1}{2}\left(B+\frac{3}{2}\right)-\frac{3}{4}B=\frac{5}{4}
Whakakapia te B+\frac{3}{2} mō te A ki tērā atu whārite, \frac{1}{2}A-\frac{3}{4}B=\frac{5}{4}.
\frac{1}{2}B+\frac{3}{4}-\frac{3}{4}B=\frac{5}{4}
Whakareatia \frac{1}{2} ki te B+\frac{3}{2}.
-\frac{1}{4}B+\frac{3}{4}=\frac{5}{4}
Tāpiri \frac{B}{2} ki te -\frac{3B}{4}.
-\frac{1}{4}B=\frac{1}{2}
Me tango \frac{3}{4} mai i ngā taha e rua o te whārite.
B=-2
Me whakarea ngā taha e rua ki te -4.
A=-2+\frac{3}{2}
Whakaurua te -2 mō B ki A=B+\frac{3}{2}. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō A hāngai tonu.
A=-\frac{1}{2}
Tāpiri \frac{3}{2} ki te -2.
A=-\frac{1}{2},B=-2
Kua oti te pūnaha te whakatau.
\frac{1}{2}A+\frac{1}{2}B-B=\frac{3}{4}
Whakaarohia te whārite tuatahi. Whakamahia te āhuatanga tohatoha hei whakarea te A+B ki te \frac{1}{2}.
\frac{1}{2}A-\frac{1}{2}B=\frac{3}{4}
Pahekotia te \frac{1}{2}B me -B, ka -\frac{1}{2}B.
\frac{1}{2}A+\frac{1}{4}B-B=\frac{5}{4}
Whakaarohia te whārite tuarua. Whakamahia te āhuatanga tohatoha hei whakarea te 2A+B ki te \frac{1}{4}.
\frac{1}{2}A-\frac{3}{4}B=\frac{5}{4}
Pahekotia te \frac{1}{4}B me -B, ka -\frac{3}{4}B.
\frac{1}{2}A-\frac{1}{2}B=\frac{3}{4},\frac{1}{2}A-\frac{3}{4}B=\frac{5}{4}
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}\frac{1}{2}&-\frac{1}{2}\\\frac{1}{2}&-\frac{3}{4}\end{matrix}\right)\left(\begin{matrix}A\\B\end{matrix}\right)=\left(\begin{matrix}\frac{3}{4}\\\frac{5}{4}\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}\frac{1}{2}&-\frac{1}{2}\\\frac{1}{2}&-\frac{3}{4}\end{matrix}\right))\left(\begin{matrix}\frac{1}{2}&-\frac{1}{2}\\\frac{1}{2}&-\frac{3}{4}\end{matrix}\right)\left(\begin{matrix}A\\B\end{matrix}\right)=inverse(\left(\begin{matrix}\frac{1}{2}&-\frac{1}{2}\\\frac{1}{2}&-\frac{3}{4}\end{matrix}\right))\left(\begin{matrix}\frac{3}{4}\\\frac{5}{4}\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}\frac{1}{2}&-\frac{1}{2}\\\frac{1}{2}&-\frac{3}{4}\end{matrix}\right).
\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}A\\B\end{matrix}\right)=inverse(\left(\begin{matrix}\frac{1}{2}&-\frac{1}{2}\\\frac{1}{2}&-\frac{3}{4}\end{matrix}\right))\left(\begin{matrix}\frac{3}{4}\\\frac{5}{4}\end{matrix}\right)
Ko te hua o tētahi poukapa me te kōaro ko te poukapa tuakiri.
\left(\begin{matrix}A\\B\end{matrix}\right)=inverse(\left(\begin{matrix}\frac{1}{2}&-\frac{1}{2}\\\frac{1}{2}&-\frac{3}{4}\end{matrix}\right))\left(\begin{matrix}\frac{3}{4}\\\frac{5}{4}\end{matrix}\right)
Whakareatia ngā poukapa kei te taha mauī o te tohu ōrite.
\left(\begin{matrix}A\\B\end{matrix}\right)=\left(\begin{matrix}-\frac{\frac{3}{4}}{\frac{1}{2}\left(-\frac{3}{4}\right)-\left(-\frac{1}{2}\times \frac{1}{2}\right)}&-\frac{-\frac{1}{2}}{\frac{1}{2}\left(-\frac{3}{4}\right)-\left(-\frac{1}{2}\times \frac{1}{2}\right)}\\-\frac{\frac{1}{2}}{\frac{1}{2}\left(-\frac{3}{4}\right)-\left(-\frac{1}{2}\times \frac{1}{2}\right)}&\frac{\frac{1}{2}}{\frac{1}{2}\left(-\frac{3}{4}\right)-\left(-\frac{1}{2}\times \frac{1}{2}\right)}\end{matrix}\right)\left(\begin{matrix}\frac{3}{4}\\\frac{5}{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}A\\B\end{matrix}\right)=\left(\begin{matrix}6&-4\\4&-4\end{matrix}\right)\left(\begin{matrix}\frac{3}{4}\\\frac{5}{4}\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}A\\B\end{matrix}\right)=\left(\begin{matrix}6\times \frac{3}{4}-4\times \frac{5}{4}\\4\times \frac{3}{4}-4\times \frac{5}{4}\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}A\\B\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{2}\\-2\end{matrix}\right)
Mahia ngā tātaitanga.
A=-\frac{1}{2},B=-2
Tangohia ngā huānga poukapa A me B.
\frac{1}{2}A+\frac{1}{2}B-B=\frac{3}{4}
Whakaarohia te whārite tuatahi. Whakamahia te āhuatanga tohatoha hei whakarea te A+B ki te \frac{1}{2}.
\frac{1}{2}A-\frac{1}{2}B=\frac{3}{4}
Pahekotia te \frac{1}{2}B me -B, ka -\frac{1}{2}B.
\frac{1}{2}A+\frac{1}{4}B-B=\frac{5}{4}
Whakaarohia te whārite tuarua. Whakamahia te āhuatanga tohatoha hei whakarea te 2A+B ki te \frac{1}{4}.
\frac{1}{2}A-\frac{3}{4}B=\frac{5}{4}
Pahekotia te \frac{1}{4}B me -B, ka -\frac{3}{4}B.
\frac{1}{2}A-\frac{1}{2}B=\frac{3}{4},\frac{1}{2}A-\frac{3}{4}B=\frac{5}{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{1}{2}A-\frac{1}{2}A-\frac{1}{2}B+\frac{3}{4}B=\frac{3-5}{4}
Me tango \frac{1}{2}A-\frac{3}{4}B=\frac{5}{4} mai i \frac{1}{2}A-\frac{1}{2}B=\frac{3}{4} mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
-\frac{1}{2}B+\frac{3}{4}B=\frac{3-5}{4}
Tāpiri \frac{A}{2} ki te -\frac{A}{2}. Ka whakakore atu ngā kupu \frac{A}{2} me -\frac{A}{2}, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.
\frac{1}{4}B=\frac{3-5}{4}
Tāpiri -\frac{B}{2} ki te \frac{3B}{4}.
\frac{1}{4}B=-\frac{1}{2}
Tāpiri \frac{3}{4} ki te -\frac{5}{4} 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.
B=-2
Me whakarea ngā taha e rua ki te 4.
\frac{1}{2}A-\frac{3}{4}\left(-2\right)=\frac{5}{4}
Whakaurua te -2 mō B ki \frac{1}{2}A-\frac{3}{4}B=\frac{5}{4}. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō A hāngai tonu.
\frac{1}{2}A+\frac{3}{2}=\frac{5}{4}
Whakareatia -\frac{3}{4} ki te -2.
\frac{1}{2}A=-\frac{1}{4}
Me tango \frac{3}{2} mai i ngā taha e rua o te whārite.
A=-\frac{1}{2}
Me whakarea ngā taha e rua ki te 2.
A=-\frac{1}{2},B=-2
Kua oti te pūnaha te whakatau.
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