Whakaoti i te {l}{a=x(96/80)}{60-a=x+10(96)}

$$\left. \begin{array} { l } { a = x ( 96 / 80 ) } \\ { 60 - a = x + 10 ( 96 ) } \end{array} \right.$$

Whakaoti mō a, x

$$x = -\frac{4500}{11} = -409\frac{1}{11} \approx -409.090909091$$

$$a = -\frac{5400}{11} = -490\frac{10}{11} \approx -490.909090909$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Whakahekea te hautanga \frac{96}{80} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 16.

$$a=x\times \frac{6}{5}$$

Tangohia te x\times \frac{6}{5} mai i ngā taha e rua.

$$a-x\times \frac{6}{5}=0$$

Whakareatia te -1 ki te \frac{6}{5}, ka -\frac{6}{5}.

$$a-\frac{6}{5}x=0$$

Whakaarohia te whārite tuarua. Whakareatia te 10 ki te 96, ka 960.

$$60-a=x+960$$

Tangohia te x mai i ngā taha e rua.

$$60-a-x=960$$

Tangohia te 60 mai i ngā taha e rua.

$$-a-x=960-60$$

Tangohia te 60 i te 960, ka 900.

$$-a-x=900$$

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.

$$a-\frac{6}{5}x=0,-a-x=900$$

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

$$a-\frac{6}{5}x=0$$

Me tāpiri \frac{6x}{5} ki ngā taha e rua o te whārite.

$$a=\frac{6}{5}x$$

Whakakapia te \frac{6x}{5} mō te a ki tērā atu whārite, -a-x=900.

$$-\frac{6}{5}x-x=900$$

Tāpiri -\frac{6x}{5} ki te -x.

$$-\frac{11}{5}x=900$$

Whakawehea ngā taha e rua o te whārite ki te -\frac{11}{5}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$x=-\frac{4500}{11}$$

Whakaurua te -\frac{4500}{11} mō x ki a=\frac{6}{5}x. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō a hāngai tonu.

$$a=\frac{6}{5}\left(-\frac{4500}{11}\right)$$

Whakareatia \frac{6}{5} ki te -\frac{4500}{11} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$a=-\frac{5400}{11}$$

Kua oti te pūnaha te whakatau.

$$a=-\frac{5400}{11},x=-\frac{4500}{11}$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Whakahekea te hautanga \frac{96}{80} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 16.

$$a=x\times \frac{6}{5}$$

Tangohia te x\times \frac{6}{5} mai i ngā taha e rua.

$$a-x\times \frac{6}{5}=0$$

Whakareatia te -1 ki te \frac{6}{5}, ka -\frac{6}{5}.

$$a-\frac{6}{5}x=0$$

Whakaarohia te whārite tuarua. Whakareatia te 10 ki te 96, ka 960.

$$60-a=x+960$$

Tangohia te x mai i ngā taha e rua.

$$60-a-x=960$$

Tangohia te 60 mai i ngā taha e rua.

$$-a-x=960-60$$

Tangohia te 60 i te 960, ka 900.

$$-a-x=900$$

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

$$a-\frac{6}{5}x=0,-a-x=900$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}1&-\frac{6}{5}\\-1&-1\end{matrix}\right)\left(\begin{matrix}a\\x\end{matrix}\right)=\left(\begin{matrix}0\\900\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&-\frac{6}{5}\\-1&-1\end{matrix}\right).

$$inverse(\left(\begin{matrix}1&-\frac{6}{5}\\-1&-1\end{matrix}\right))\left(\begin{matrix}1&-\frac{6}{5}\\-1&-1\end{matrix}\right)\left(\begin{matrix}a\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-\frac{6}{5}\\-1&-1\end{matrix}\right))\left(\begin{matrix}0\\900\end{matrix}\right)$$

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

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}a\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-\frac{6}{5}\\-1&-1\end{matrix}\right))\left(\begin{matrix}0\\900\end{matrix}\right)$$

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

$$\left(\begin{matrix}a\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-\frac{6}{5}\\-1&-1\end{matrix}\right))\left(\begin{matrix}0\\900\end{matrix}\right)$$

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.

$$\left(\begin{matrix}a\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{-1-\left(-\frac{6}{5}\left(-1\right)\right)}&-\frac{-\frac{6}{5}}{-1-\left(-\frac{6}{5}\left(-1\right)\right)}\\-\frac{-1}{-1-\left(-\frac{6}{5}\left(-1\right)\right)}&\frac{1}{-1-\left(-\frac{6}{5}\left(-1\right)\right)}\end{matrix}\right)\left(\begin{matrix}0\\900\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}a\\x\end{matrix}\right)=\left(\begin{matrix}\frac{5}{11}&-\frac{6}{11}\\-\frac{5}{11}&-\frac{5}{11}\end{matrix}\right)\left(\begin{matrix}0\\900\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}a\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{6}{11}\times 900\\-\frac{5}{11}\times 900\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}a\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{5400}{11}\\-\frac{4500}{11}\end{matrix}\right)$$

Tangohia ngā huānga poukapa a me x.

$$a=-\frac{5400}{11},x=-\frac{4500}{11}$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Whakahekea te hautanga \frac{96}{80} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 16.

$$a=x\times \frac{6}{5}$$

Tangohia te x\times \frac{6}{5} mai i ngā taha e rua.

$$a-x\times \frac{6}{5}=0$$

Whakareatia te -1 ki te \frac{6}{5}, ka -\frac{6}{5}.

$$a-\frac{6}{5}x=0$$

Whakaarohia te whārite tuarua. Whakareatia te 10 ki te 96, ka 960.

$$60-a=x+960$$

Tangohia te x mai i ngā taha e rua.

$$60-a-x=960$$

Tangohia te 60 mai i ngā taha e rua.

$$-a-x=960-60$$

Tangohia te 60 i te 960, ka 900.

$$-a-x=900$$

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.

$$a-\frac{6}{5}x=0,-a-x=900$$

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.

$$-a-\left(-\frac{6}{5}x\right)=0,-a-x=900$$

Whakarūnātia.

$$-a+\frac{6}{5}x=0,-a-x=900$$

Me tango -a-x=900 mai i -a+\frac{6}{5}x=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$-a+a+\frac{6}{5}x+x=-900$$

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.

$$\frac{6}{5}x+x=-900$$

Tāpiri \frac{6x}{5} ki te x.

$$\frac{11}{5}x=-900$$

Whakawehea ngā taha e rua o te whārite ki te \frac{11}{5}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$x=-\frac{4500}{11}$$

Whakaurua te -\frac{4500}{11} mō x ki -a-x=900. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō a hāngai tonu.

$$-a-\left(-\frac{4500}{11}\right)=900$$

Me tango \frac{4500}{11} mai i ngā taha e rua o te whārite.

$$-a=\frac{5400}{11}$$

Whakawehea ngā taha e rua ki te -1.

$$a=-\frac{5400}{11}$$

Kua oti te pūnaha te whakatau.

$$a=-\frac{5400}{11},x=-\frac{4500}{11}$$