Whakaoti i te {l}{x=y/3}{y=2x}

$$\left. \begin{array} { l } { x = \frac { y } { 3 } } \\ { y = 2 x } \end{array} \right.$$

Whakaoti mō x, y

$$x=0$$

$$y=0$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Tangohia te \frac{y}{3} mai i ngā taha e rua.

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

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

$$3x-y=0$$

Whakaarohia te whārite tuarua. Tangohia te 2x mai i ngā taha e rua.

$$y-2x=0$$

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.

$$3x-y=0,-2x+y=0$$

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

$$3x-y=0$$

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

$$3x=y$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{1}{3}y$$

Whakakapia te \frac{y}{3} mō te x ki tērā atu whārite, -2x+y=0.

$$-2\times \frac{1}{3}y+y=0$$

Whakareatia -2 ki te \frac{y}{3}.

$$-\frac{2}{3}y+y=0$$

Tāpiri -\frac{2y}{3} ki te y.

$$\frac{1}{3}y=0$$

Me whakarea ngā taha e rua ki te 3.

$$y=0$$

Whakaurua te 0 mō y ki x=\frac{1}{3}y. 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. Tangohia te \frac{y}{3} mai i ngā taha e rua.

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

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

$$3x-y=0$$

Whakaarohia te whārite tuarua. Tangohia te 2x mai i ngā taha e rua.

$$y-2x=0$$

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

$$3x-y=0,-2x+y=0$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}3&-1\\-2&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}0\\0\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}3&-1\\-2&1\end{matrix}\right).

$$inverse(\left(\begin{matrix}3&-1\\-2&1\end{matrix}\right))\left(\begin{matrix}3&-1\\-2&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}3&-1\\-2&1\end{matrix}\right))\left(\begin{matrix}0\\0\end{matrix}\right)$$

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

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}3&-1\\-2&1\end{matrix}\right))\left(\begin{matrix}0\\0\end{matrix}\right)$$

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

$$\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}3&-1\\-2&1\end{matrix}\right))\left(\begin{matrix}0\\0\end{matrix}\right)$$

Mō te poukapa 2\times 2 \left(\begin{matrix}a&b\\c&d\end{matrix}\right), ko te \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.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{3-\left(-\left(-2\right)\right)}&-\frac{-1}{3-\left(-\left(-2\right)\right)}\\-\frac{-2}{3-\left(-\left(-2\right)\right)}&\frac{3}{3-\left(-\left(-2\right)\right)}\end{matrix}\right)\left(\begin{matrix}0\\0\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}1&1\\2&3\end{matrix}\right)\left(\begin{matrix}0\\0\end{matrix}\right)$$

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. Tangohia te \frac{y}{3} mai i ngā taha e rua.

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

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

$$3x-y=0$$

Whakaarohia te whārite tuarua. Tangohia te 2x mai i ngā taha e rua.

$$y-2x=0$$

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.

$$3x-y=0,-2x+y=0$$

Kia ōrite ai a 3x me -2x, 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 3.

$$-2\times 3x-2\left(-1\right)y=0,3\left(-2\right)x+3y=0$$

Whakarūnātia.

$$-6x+2y=0,-6x+3y=0$$

Me tango -6x+3y=0 mai i -6x+2y=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$-6x+6x+2y-3y=0$$

Tāpiri -6x ki te 6x. Ka whakakore atu ngā kupu -6x me 6x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.

$$2y-3y=0$$

Tāpiri 2y ki te -3y.

$$-y=0$$

Whakawehea ngā taha e rua ki te -1.

$$y=0$$

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

$$-2x=0$$

Whakawehea ngā taha e rua ki te -2.

$$x=0$$

Kua oti te pūnaha te whakatau.

$$x=0,y=0$$