Whakaoti i te {l}{x=3y(-10)}{y=x/3(-10)}

$$\left. \begin{array} { l } { x = 3 y ( - 10 ) } \\ { y = \frac { x } { 3 } ( - 10 ) } \end{array} \right.$$

Whakaoti mō x, y

$$x=0$$

$$y=0$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Whakareatia te 3 ki te -10, ka -30.

$$x=-30y$$

Whakakapia te -30y mō te x ki tērā atu whārite, 10x+3y=0.

$$10\left(-30\right)y+3y=0$$

Whakareatia 10 ki te -30y.

$$-300y+3y=0$$

Tāpiri -300y ki te 3y.

$$-297y=0$$

Whakawehea ngā taha e rua ki te -297.

$$y=0$$

Whakaurua te 0 mō y ki x=-30y. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$x=0$$

Kua oti te pūnaha te whakatau.

$$x=0,y=0$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Whakareatia te 3 ki te -10, ka -30.

$$x=-30y$$

Me tāpiri te 30y ki ngā taha e rua.

$$x+30y=0$$

Whakaarohia te whārite tuarua. Tuhia te \frac{x}{3}\left(-10\right) hei hautanga kotahi.

$$y=\frac{-x\times 10}{3}$$

Whakareatia te -1 ki te 10, ka -10.

$$y=\frac{-10x}{3}$$

Tangohia te \frac{-10x}{3} mai i ngā taha e rua.

$$y-\frac{-10x}{3}=0$$

Whakareatia ngā taha e rua o te whārite ki te 3.

$$3y+10x=0$$

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

$$x+30y=0,10x+3y=0$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}1&30\\10&3\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}0\\0\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&30\\10&3\end{matrix}\right).

$$inverse(\left(\begin{matrix}1&30\\10&3\end{matrix}\right))\left(\begin{matrix}1&30\\10&3\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&30\\10&3\end{matrix}\right))\left(\begin{matrix}0\\0\end{matrix}\right)$$

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

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&30\\10&3\end{matrix}\right))\left(\begin{matrix}0\\0\end{matrix}\right)$$

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

$$\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&30\\10&3\end{matrix}\right))\left(\begin{matrix}0\\0\end{matrix}\right)$$

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.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{3}{3-30\times 10}&-\frac{30}{3-30\times 10}\\-\frac{10}{3-30\times 10}&\frac{1}{3-30\times 10}\end{matrix}\right)\left(\begin{matrix}0\\0\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{99}&\frac{10}{99}\\\frac{10}{297}&-\frac{1}{297}\end{matrix}\right)\left(\begin{matrix}0\\0\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}0\\0\end{matrix}\right)$$

Tangohia ngā huānga poukapa x me y.

$$x=0,y=0$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Whakareatia te 3 ki te -10, ka -30.

$$x=-30y$$

Me tāpiri te 30y ki ngā taha e rua.

$$x+30y=0$$

Whakaarohia te whārite tuarua. Tuhia te \frac{x}{3}\left(-10\right) hei hautanga kotahi.

$$y=\frac{-x\times 10}{3}$$

Whakareatia te -1 ki te 10, ka -10.

$$y=\frac{-10x}{3}$$

Tangohia te \frac{-10x}{3} mai i ngā taha e rua.

$$y-\frac{-10x}{3}=0$$

Whakareatia ngā taha e rua o te whārite ki te 3.

$$3y+10x=0$$

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.

$$x+30y=0,10x+3y=0$$

Kia ōrite ai a x me 10x, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te 10 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 1.

$$10x+10\times 30y=0,10x+3y=0$$

Whakarūnātia.

$$10x+300y=0,10x+3y=0$$

Me tango 10x+3y=0 mai i 10x+300y=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$10x-10x+300y-3y=0$$

Tāpiri 10x ki te -10x. Ka whakakore atu ngā kupu 10x me -10x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.

$$300y-3y=0$$

Tāpiri 300y ki te -3y.

$$297y=0$$

Whakawehea ngā taha e rua ki te 297.

$$y=0$$

Whakaurua te 0 mō y ki 10x+3y=0. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$10x=0$$

Whakawehea ngā taha e rua ki te 10.

$$x=0$$

Kua oti te pūnaha te whakatau.

$$x=0,y=0$$