Whakaoti i te y=-2x,y=x/2

$$y = - 2 x , y = \frac { x } { 2 }$$

Whakaoti mō y, x

$$x=0$$

$$y=0$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Me tāpiri te 2x ki ngā taha e rua.

$$y+2x=0$$

Whakaarohia te whārite tuarua. Tangohia te \frac{x}{2} mai i ngā taha e rua.

$$y-\frac{x}{2}=0$$

Whakareatia ngā taha e rua o te whārite ki te 2.

$$2y-x=0$$

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.

$$y+2x=0,2y-x=0$$

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

$$y+2x=0$$

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

$$y=-2x$$

Whakakapia te -2x mō te y ki tērā atu whārite, 2y-x=0.

$$2\left(-2\right)x-x=0$$

Whakareatia 2 ki te -2x.

$$-4x-x=0$$

Tāpiri -4x ki te -x.

$$-5x=0$$

Whakawehea ngā taha e rua ki te -5.

$$x=0$$

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

$$y=0$$

Kua oti te pūnaha te whakatau.

$$y=0,x=0$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Me tāpiri te 2x ki ngā taha e rua.

$$y+2x=0$$

Whakaarohia te whārite tuarua. Tangohia te \frac{x}{2} mai i ngā taha e rua.

$$y-\frac{x}{2}=0$$

Whakareatia ngā taha e rua o te whārite ki te 2.

$$2y-x=0$$

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

$$y+2x=0,2y-x=0$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}1&2\\2&-1\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}0\\0\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&2\\2&-1\end{matrix}\right).

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

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

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

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

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

Mō te poukapa 2\times 2 \left(\begin{matrix}a&b\\c&d\end{matrix}\right), ko te poukapa kōaro ko \left(\begin{matrix}\frac{d}{ad-bc}&\frac{-b}{ad-bc}\\\frac{-c}{ad-bc}&\frac{a}{ad-bc}\end{matrix}\right), kia tuhia anō ai te whārite poukapa hei rapanga whakarea poukapa.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{-1-2\times 2}&-\frac{2}{-1-2\times 2}\\-\frac{2}{-1-2\times 2}&\frac{1}{-1-2\times 2}\end{matrix}\right)\left(\begin{matrix}0\\0\end{matrix}\right)$$

Mahia ngā tātaitanga.

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

Whakareatia ngā poukapa.

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

Tangohia ngā huānga poukapa y me x.

$$y=0,x=0$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Me tāpiri te 2x ki ngā taha e rua.

$$y+2x=0$$

Whakaarohia te whārite tuarua. Tangohia te \frac{x}{2} mai i ngā taha e rua.

$$y-\frac{x}{2}=0$$

Whakareatia ngā taha e rua o te whārite ki te 2.

$$2y-x=0$$

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.

$$y+2x=0,2y-x=0$$

Kia ōrite ai a y me 2y, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te 2 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 1.

$$2y+2\times 2x=0,2y-x=0$$

Whakarūnātia.

$$2y+4x=0,2y-x=0$$

Me tango 2y-x=0 mai i 2y+4x=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$2y-2y+4x+x=0$$

Tāpiri 2y ki te -2y. Ka whakakore atu ngā kupu 2y me -2y, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.

$$4x+x=0$$

Tāpiri 4x ki te x.

$$5x=0$$

Whakawehea ngā taha e rua ki te 5.

$$x=0$$

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

$$2y=0$$

Whakawehea ngā taha e rua ki te 2.

$$y=0$$

Kua oti te pūnaha te whakatau.

$$y=0,x=0$$