Whakaoti i te {l}{3b=2b-a+2}{b-a=2}

$$\left\{ \begin{array} { l } { 3 b = 2 b - a + 2 } \\ { b - a = 2 } \end{array} \right.$$

Whakaoti mō b, a

$$b=2$$

$$a=0$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Tangohia te 2b mai i ngā taha e rua.

$$3b-2b=-a+2$$

Pahekotia te 3b me -2b, ka b.

$$b=-a+2$$

Whakakapia te -a+2 mō te b ki tērā atu whārite, b-a=2.

$$-a+2-a=2$$

Tāpiri -a ki te -a.

$$-2a+2=2$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$-2a=0$$

Whakawehea ngā taha e rua ki te -2.

$$a=0$$

Whakaurua te 0 mō a ki b=-a+2. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō b hāngai tonu.

$$b=2$$

Kua oti te pūnaha te whakatau.

$$b=2,a=0$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Tangohia te 2b mai i ngā taha e rua.

$$3b-2b=-a+2$$

Pahekotia te 3b me -2b, ka b.

$$b=-a+2$$

Me tāpiri te a ki ngā taha e rua.

$$b+a=2$$

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

$$b+a=2,b-a=2$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}1&1\\1&-1\end{matrix}\right)\left(\begin{matrix}b\\a\end{matrix}\right)=\left(\begin{matrix}2\\2\end{matrix}\right)$$

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

$$inverse(\left(\begin{matrix}1&1\\1&-1\end{matrix}\right))\left(\begin{matrix}1&1\\1&-1\end{matrix}\right)\left(\begin{matrix}b\\a\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\1&-1\end{matrix}\right))\left(\begin{matrix}2\\2\end{matrix}\right)$$

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

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}b\\a\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\1&-1\end{matrix}\right))\left(\begin{matrix}2\\2\end{matrix}\right)$$

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

$$\left(\begin{matrix}b\\a\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\1&-1\end{matrix}\right))\left(\begin{matrix}2\\2\end{matrix}\right)$$

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.

$$\left(\begin{matrix}b\\a\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{-1-1}&-\frac{1}{-1-1}\\-\frac{1}{-1-1}&\frac{1}{-1-1}\end{matrix}\right)\left(\begin{matrix}2\\2\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}b\\a\end{matrix}\right)=\left(\begin{matrix}\frac{1}{2}&\frac{1}{2}\\\frac{1}{2}&-\frac{1}{2}\end{matrix}\right)\left(\begin{matrix}2\\2\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}b\\a\end{matrix}\right)=\left(\begin{matrix}\frac{1}{2}\times 2+\frac{1}{2}\times 2\\\frac{1}{2}\times 2-\frac{1}{2}\times 2\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}b\\a\end{matrix}\right)=\left(\begin{matrix}2\\0\end{matrix}\right)$$

Tangohia ngā huānga poukapa b me a.

$$b=2,a=0$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Tangohia te 2b mai i ngā taha e rua.

$$3b-2b=-a+2$$

Pahekotia te 3b me -2b, ka b.

$$b=-a+2$$

Me tāpiri te a ki ngā taha e rua.

$$b+a=2$$

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.

$$b+a=2,b-a=2$$

Me tango b-a=2 mai i b+a=2 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$b-b+a+a=2-2$$

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

$$a+a=2-2$$

Tāpiri a ki te a.

$$2a=2-2$$

Tāpiri 2 ki te -2.

$$2a=0$$

Whakawehea ngā taha e rua ki te 2.

$$a=0$$

Whakaurua te 0 mō a ki b-a=2. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō b hāngai tonu.

$$b=2$$

Kua oti te pūnaha te whakatau.

$$b=2,a=0$$