Whakaoti i te {l}{a=x(96/6)}{160-a=x+10(96/60)}

$$\left. \begin{array} { l } { a = x ( 96 / 6 ) } \\ { 160 - a = x + 10 ( 96 / 60 ) } \end{array} \right.$$

Whakaoti mō a, x

$$x = \frac{160}{17} = 9\frac{7}{17} \approx 9.411764706$$

$$a = \frac{2560}{17} = 150\frac{10}{17} \approx 150.588235294$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Whakawehea te 96 ki te 6, kia riro ko 16.

$$a=x\times 16$$

Tangohia te x\times 16 mai i ngā taha e rua.

$$a-x\times 16=0$$

Whakareatia te -1 ki te 16, ka -16.

$$a-16x=0$$

Whakaarohia te whārite tuarua. Whakawehea te 96 ki te 6, kia riro ko 16.

$$160-a=x+10\times 16\times 0$$

Whakareatia te 10 ki te 16, ka 160.

$$160-a=x+160\times 0$$

Whakareatia te 160 ki te 0, ka 0.

$$160-a=x+0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$160-a=x$$

Tangohia te x mai i ngā taha e rua.

$$160-a-x=0$$

Tangohia te 160 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-a-x=-160$$

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.

$$a-16x=0,-a-x=-160$$

Kōwhiria tētahi o ngā whārite ka whakaotia mō te a mā te wehe i te a i te taha mauī o te tohu ōrite.

$$a-16x=0$$

Me tāpiri 16x ki ngā taha e rua o te whārite.

$$a=16x$$

Whakakapia te 16x mō te a ki tērā atu whārite, -a-x=-160.

$$-16x-x=-160$$

Tāpiri -16x ki te -x.

$$-17x=-160$$

Whakawehea ngā taha e rua ki te -17.

$$x=\frac{160}{17}$$

Whakaurua te \frac{160}{17} mō x ki a=16x. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō a hāngai tonu.

$$a=16\times \frac{160}{17}$$

Whakareatia 16 ki te \frac{160}{17}.

$$a=\frac{2560}{17}$$

Kua oti te pūnaha te whakatau.

$$a=\frac{2560}{17},x=\frac{160}{17}$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Whakawehea te 96 ki te 6, kia riro ko 16.

$$a=x\times 16$$

Tangohia te x\times 16 mai i ngā taha e rua.

$$a-x\times 16=0$$

Whakareatia te -1 ki te 16, ka -16.

$$a-16x=0$$

Whakaarohia te whārite tuarua. Whakawehea te 96 ki te 6, kia riro ko 16.

$$160-a=x+10\times 16\times 0$$

Whakareatia te 10 ki te 16, ka 160.

$$160-a=x+160\times 0$$

Whakareatia te 160 ki te 0, ka 0.

$$160-a=x+0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$160-a=x$$

Tangohia te x mai i ngā taha e rua.

$$160-a-x=0$$

Tangohia te 160 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-a-x=-160$$

Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.

$$a-16x=0,-a-x=-160$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}1&-16\\-1&-1\end{matrix}\right)\left(\begin{matrix}a\\x\end{matrix}\right)=\left(\begin{matrix}0\\-160\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&-16\\-1&-1\end{matrix}\right).

$$inverse(\left(\begin{matrix}1&-16\\-1&-1\end{matrix}\right))\left(\begin{matrix}1&-16\\-1&-1\end{matrix}\right)\left(\begin{matrix}a\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-16\\-1&-1\end{matrix}\right))\left(\begin{matrix}0\\-160\end{matrix}\right)$$

Ko te hua o tētahi poukapa me te kōaro ko te poukapa tuakiri.

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}a\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-16\\-1&-1\end{matrix}\right))\left(\begin{matrix}0\\-160\end{matrix}\right)$$

Whakareatia ngā poukapa kei te taha mauī o te tohu ōrite.

$$\left(\begin{matrix}a\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-16\\-1&-1\end{matrix}\right))\left(\begin{matrix}0\\-160\end{matrix}\right)$$

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.

$$\left(\begin{matrix}a\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{-1-\left(-16\left(-1\right)\right)}&-\frac{-16}{-1-\left(-16\left(-1\right)\right)}\\-\frac{-1}{-1-\left(-16\left(-1\right)\right)}&\frac{1}{-1-\left(-16\left(-1\right)\right)}\end{matrix}\right)\left(\begin{matrix}0\\-160\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}a\\x\end{matrix}\right)=\left(\begin{matrix}\frac{1}{17}&-\frac{16}{17}\\-\frac{1}{17}&-\frac{1}{17}\end{matrix}\right)\left(\begin{matrix}0\\-160\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}a\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{16}{17}\left(-160\right)\\-\frac{1}{17}\left(-160\right)\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}a\\x\end{matrix}\right)=\left(\begin{matrix}\frac{2560}{17}\\\frac{160}{17}\end{matrix}\right)$$

Tangohia ngā huānga poukapa a me x.

$$a=\frac{2560}{17},x=\frac{160}{17}$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Whakawehea te 96 ki te 6, kia riro ko 16.

$$a=x\times 16$$

Tangohia te x\times 16 mai i ngā taha e rua.

$$a-x\times 16=0$$

Whakareatia te -1 ki te 16, ka -16.

$$a-16x=0$$

Whakaarohia te whārite tuarua. Whakawehea te 96 ki te 6, kia riro ko 16.

$$160-a=x+10\times 16\times 0$$

Whakareatia te 10 ki te 16, ka 160.

$$160-a=x+160\times 0$$

Whakareatia te 160 ki te 0, ka 0.

$$160-a=x+0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$160-a=x$$

Tangohia te x mai i ngā taha e rua.

$$160-a-x=0$$

Tangohia te 160 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-a-x=-160$$

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.

$$a-16x=0,-a-x=-160$$

Kia ōrite ai a a me -a, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te -1 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 1.

$$-a-\left(-16x\right)=0,-a-x=-160$$

Whakarūnātia.

$$-a+16x=0,-a-x=-160$$

Me tango -a-x=-160 mai i -a+16x=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$-a+a+16x+x=160$$

Tāpiri -a ki te a. Ka whakakore atu ngā kupu -a me a, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.

$$16x+x=160$$

Tāpiri 16x ki te x.

$$17x=160$$

Whakawehea ngā taha e rua ki te 17.

$$x=\frac{160}{17}$$

Whakaurua te \frac{160}{17} mō x ki -a-x=-160. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō a hāngai tonu.

$$-a-\frac{160}{17}=-160$$

Me tāpiri \frac{160}{17} ki ngā taha e rua o te whārite.

$$-a=-\frac{2560}{17}$$

Whakawehea ngā taha e rua ki te -1.

$$a=\frac{2560}{17}$$

Kua oti te pūnaha te whakatau.

$$a=\frac{2560}{17},x=\frac{160}{17}$$