Whakaoti i te {l}{4*4k+b=0}{3*6k+b=0.2}

$$\left\{ \begin{array} { l } { 4 \cdot 4 k + b = 0 } \\ { 3 \cdot 6 k + b = 0.2 } \end{array} \right.$$

Whakaoti mō k, b

$$k=0.1$$

$$b=-1.6$$

Ngā Upane e Whakamahi ana i te Whakakapinga

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.

$$16k+b=0,18k+b=0.2$$

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

$$16k+b=0$$

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

$$16k=-b$$

Whakawehea ngā taha e rua ki te 16.

$$k=\frac{1}{16}\left(-1\right)b$$

Whakareatia \frac{1}{16} ki te -b.

$$k=-\frac{1}{16}b$$

Whakakapia te -\frac{b}{16} mō te k ki tērā atu whārite, 18k+b=0.2.

$$18\left(-\frac{1}{16}\right)b+b=0.2$$

Whakareatia 18 ki te -\frac{b}{16}.

$$-\frac{9}{8}b+b=0.2$$

Tāpiri -\frac{9b}{8} ki te b.

$$-\frac{1}{8}b=0.2$$

Me whakarea ngā taha e rua ki te -8.

$$b=-\frac{8}{5}$$

Whakaurua te -\frac{8}{5} mō b ki k=-\frac{1}{16}b. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō k hāngai tonu.

$$k=-\frac{1}{16}\left(-\frac{8}{5}\right)$$

Whakareatia -\frac{1}{16} ki te -\frac{8}{5} 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.

$$k=\frac{1}{10}$$

Kua oti te pūnaha te whakatau.

$$k=\frac{1}{10},b=-\frac{8}{5}$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

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

$$16k+b=0,18k+b=0.2$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}16&1\\18&1\end{matrix}\right)\left(\begin{matrix}k\\b\end{matrix}\right)=\left(\begin{matrix}0\\0.2\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}16&1\\18&1\end{matrix}\right).

$$inverse(\left(\begin{matrix}16&1\\18&1\end{matrix}\right))\left(\begin{matrix}16&1\\18&1\end{matrix}\right)\left(\begin{matrix}k\\b\end{matrix}\right)=inverse(\left(\begin{matrix}16&1\\18&1\end{matrix}\right))\left(\begin{matrix}0\\0.2\end{matrix}\right)$$

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

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}k\\b\end{matrix}\right)=inverse(\left(\begin{matrix}16&1\\18&1\end{matrix}\right))\left(\begin{matrix}0\\0.2\end{matrix}\right)$$

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

$$\left(\begin{matrix}k\\b\end{matrix}\right)=inverse(\left(\begin{matrix}16&1\\18&1\end{matrix}\right))\left(\begin{matrix}0\\0.2\end{matrix}\right)$$

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.

$$\left(\begin{matrix}k\\b\end{matrix}\right)=\left(\begin{matrix}\frac{1}{16-18}&-\frac{1}{16-18}\\-\frac{18}{16-18}&\frac{16}{16-18}\end{matrix}\right)\left(\begin{matrix}0\\0.2\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}k\\b\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{2}&\frac{1}{2}\\9&-8\end{matrix}\right)\left(\begin{matrix}0\\0.2\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}k\\b\end{matrix}\right)=\left(\begin{matrix}\frac{1}{2}\times 0.2\\-8\times 0.2\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}k\\b\end{matrix}\right)=\left(\begin{matrix}\frac{1}{10}\\-1.6\end{matrix}\right)$$

Tangohia ngā huānga poukapa k me b.

$$k=\frac{1}{10},b=-1.6$$

Ngā Upane e Whakamahi i te Tangohanga

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.

$$16k+b=0,18k+b=0.2$$

Me tango 18k+b=0.2 mai i 16k+b=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$16k-18k+b-b=-0.2$$

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.

$$16k-18k=-0.2$$

Tāpiri 16k ki te -18k.

$$-2k=-0.2$$

Whakawehea ngā taha e rua ki te -2.

$$k=\frac{1}{10}$$

Whakaurua te \frac{1}{10} mō k ki 18k+b=0.2. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō b hāngai tonu.

$$18\times \frac{1}{10}+b=0.2$$

Whakareatia 18 ki te \frac{1}{10}.

$$\frac{9}{5}+b=0.2$$

Me tango \frac{9}{5} mai i ngā taha e rua o te whārite.

$$b=-\frac{8}{5}$$

Kua oti te pūnaha te whakatau.

$$k=\frac{1}{10},b=-\frac{8}{5}$$