Whakaoti i te {l}{a=b}{a+b=5}

$$\left. \begin{array} { l } { a = b } \\ { a + b = 5 } \end{array} \right.$$

Whakaoti mō a, b

$$a = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$b = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Ngā Upane e Whakamahi ana i te Whakakapinga

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

$$a-b=0$$

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.

$$a-b=0,a+b=5$$

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

$$a-b=0$$

Me tāpiri b ki ngā taha e rua o te whārite.

$$a=b$$

Whakakapia te b mō te a ki tērā atu whārite, a+b=5.

$$b+b=5$$

Tāpiri b ki te b.

$$2b=5$$

Whakawehea ngā taha e rua ki te 2.

$$b=\frac{5}{2}$$

Whakaurua te \frac{5}{2} mō b ki a=b. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō a hāngai tonu.

$$a=\frac{5}{2}$$

Kua oti te pūnaha te whakatau.

$$a=\frac{5}{2},b=\frac{5}{2}$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

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

$$a-b=0$$

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

$$a-b=0,a+b=5$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}1&-1\\1&1\end{matrix}\right)\left(\begin{matrix}a\\b\end{matrix}\right)=\left(\begin{matrix}0\\5\end{matrix}\right)$$

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

$$inverse(\left(\begin{matrix}1&-1\\1&1\end{matrix}\right))\left(\begin{matrix}1&-1\\1&1\end{matrix}\right)\left(\begin{matrix}a\\b\end{matrix}\right)=inverse(\left(\begin{matrix}1&-1\\1&1\end{matrix}\right))\left(\begin{matrix}0\\5\end{matrix}\right)$$

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

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}a\\b\end{matrix}\right)=inverse(\left(\begin{matrix}1&-1\\1&1\end{matrix}\right))\left(\begin{matrix}0\\5\end{matrix}\right)$$

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

$$\left(\begin{matrix}a\\b\end{matrix}\right)=inverse(\left(\begin{matrix}1&-1\\1&1\end{matrix}\right))\left(\begin{matrix}0\\5\end{matrix}\right)$$

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.

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

Mahia ngā tātaitanga.

$$\left(\begin{matrix}a\\b\end{matrix}\right)=\left(\begin{matrix}\frac{1}{2}&\frac{1}{2}\\-\frac{1}{2}&\frac{1}{2}\end{matrix}\right)\left(\begin{matrix}0\\5\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}a\\b\end{matrix}\right)=\left(\begin{matrix}\frac{1}{2}\times 5\\\frac{1}{2}\times 5\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}a\\b\end{matrix}\right)=\left(\begin{matrix}\frac{5}{2}\\\frac{5}{2}\end{matrix}\right)$$

Tangohia ngā huānga poukapa a me b.

$$a=\frac{5}{2},b=\frac{5}{2}$$

Ngā Upane e Whakamahi i te Tangohanga

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

$$a-b=0$$

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.

$$a-b=0,a+b=5$$

Me tango a+b=5 mai i a-b=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$a-a-b-b=-5$$

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.

$$-b-b=-5$$

Tāpiri -b ki te -b.

$$-2b=-5$$

Whakawehea ngā taha e rua ki te -2.

$$b=\frac{5}{2}$$

Whakaurua te \frac{5}{2} mō b ki a+b=5. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō a hāngai tonu.

$$a+\frac{5}{2}=5$$

Me tango \frac{5}{2} mai i ngā taha e rua o te whārite.

$$a=\frac{5}{2}$$

Kua oti te pūnaha te whakatau.

$$a=\frac{5}{2},b=\frac{5}{2}$$