Whakaoti i te {l}{y=376x}{2y=32x}

$$\left. \begin{array} { l } { y = 376 x } \\ { 2 y = 32 x } \end{array} \right.$$

Whakaoti mō y, x

$$x=0$$

$$y=0$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Tangohia te 376x mai i ngā taha e rua.

$$y-376x=0$$

Whakaarohia te whārite tuarua. Tangohia te 32x mai i ngā taha e rua.

$$2y-32x=0$$

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.

$$y-376x=0,2y-32x=0$$

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

$$y-376x=0$$

Me tāpiri 376x ki ngā taha e rua o te whārite.

$$y=376x$$

Whakakapia te 376x mō te y ki tērā atu whārite, 2y-32x=0.

$$2\times 376x-32x=0$$

Whakareatia 2 ki te 376x.

$$752x-32x=0$$

Tāpiri 752x ki te -32x.

$$720x=0$$

Whakawehea ngā taha e rua ki te 720.

$$x=0$$

Whakaurua te 0 mō x ki y=376x. 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. Tangohia te 376x mai i ngā taha e rua.

$$y-376x=0$$

Whakaarohia te whārite tuarua. Tangohia te 32x mai i ngā taha e rua.

$$2y-32x=0$$

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

$$y-376x=0,2y-32x=0$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}1&-376\\2&-32\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}0\\0\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&-376\\2&-32\end{matrix}\right).

$$inverse(\left(\begin{matrix}1&-376\\2&-32\end{matrix}\right))\left(\begin{matrix}1&-376\\2&-32\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-376\\2&-32\end{matrix}\right))\left(\begin{matrix}0\\0\end{matrix}\right)$$

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

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-376\\2&-32\end{matrix}\right))\left(\begin{matrix}0\\0\end{matrix}\right)$$

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

$$\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-376\\2&-32\end{matrix}\right))\left(\begin{matrix}0\\0\end{matrix}\right)$$

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.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{32}{-32-\left(-376\times 2\right)}&-\frac{-376}{-32-\left(-376\times 2\right)}\\-\frac{2}{-32-\left(-376\times 2\right)}&\frac{1}{-32-\left(-376\times 2\right)}\end{matrix}\right)\left(\begin{matrix}0\\0\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{2}{45}&\frac{47}{90}\\-\frac{1}{360}&\frac{1}{720}\end{matrix}\right)\left(\begin{matrix}0\\0\end{matrix}\right)$$

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. Tangohia te 376x mai i ngā taha e rua.

$$y-376x=0$$

Whakaarohia te whārite tuarua. Tangohia te 32x mai i ngā taha e rua.

$$2y-32x=0$$

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.

$$y-376x=0,2y-32x=0$$

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.

$$2y+2\left(-376\right)x=0,2y-32x=0$$

Whakarūnātia.

$$2y-752x=0,2y-32x=0$$

Me tango 2y-32x=0 mai i 2y-752x=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$2y-2y-752x+32x=0$$

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.

$$-752x+32x=0$$

Tāpiri -752x ki te 32x.

$$-720x=0$$

Whakawehea ngā taha e rua ki te -720.

$$x=0$$

Whakaurua te 0 mō x ki 2y-32x=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.

$$y=0,x=0$$