Whakaoti i te 4x+2y=0quadtext{D)}6x-2y=0

$$4 x + 2 y = 0 \quad \text { D) } 6 x - 2 y = 0$$

Whakaoti mō x, y

$$x=0$$

$$y=0$$

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.

$$4x+2y=0,6x-2y=0$$

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

$$4x+2y=0$$

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

$$4x=-2y$$

Whakawehea ngā taha e rua ki te 4.

$$x=\frac{1}{4}\left(-2\right)y$$

Whakareatia \frac{1}{4} ki te -2y.

$$x=-\frac{1}{2}y$$

Whakakapia te -\frac{y}{2} mō te x ki tērā atu whārite, 6x-2y=0.

$$6\left(-\frac{1}{2}\right)y-2y=0$$

Whakareatia 6 ki te -\frac{y}{2}.

$$-3y-2y=0$$

Tāpiri -3y ki te -2y.

$$-5y=0$$

Whakawehea ngā taha e rua ki te -5.

$$y=0$$

Whakaurua te 0 mō y ki x=-\frac{1}{2}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

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

$$4x+2y=0,6x-2y=0$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}4&2\\6&-2\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}0\\0\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}4&2\\6&-2\end{matrix}\right).

$$inverse(\left(\begin{matrix}4&2\\6&-2\end{matrix}\right))\left(\begin{matrix}4&2\\6&-2\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}4&2\\6&-2\end{matrix}\right))\left(\begin{matrix}0\\0\end{matrix}\right)$$

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

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}4&2\\6&-2\end{matrix}\right))\left(\begin{matrix}0\\0\end{matrix}\right)$$

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

$$\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}4&2\\6&-2\end{matrix}\right))\left(\begin{matrix}0\\0\end{matrix}\right)$$

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.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{2}{4\left(-2\right)-2\times 6}&-\frac{2}{4\left(-2\right)-2\times 6}\\-\frac{6}{4\left(-2\right)-2\times 6}&\frac{4}{4\left(-2\right)-2\times 6}\end{matrix}\right)\left(\begin{matrix}0\\0\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{10}&\frac{1}{10}\\\frac{3}{10}&-\frac{1}{5}\end{matrix}\right)\left(\begin{matrix}0\\0\end{matrix}\right)$$

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

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.

$$4x+2y=0,6x-2y=0$$

Kia ōrite ai a 4x me 6x, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te 6 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 4.

$$6\times 4x+6\times 2y=0,4\times 6x+4\left(-2\right)y=0$$

Whakarūnātia.

$$24x+12y=0,24x-8y=0$$

Me tango 24x-8y=0 mai i 24x+12y=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$24x-24x+12y+8y=0$$

Tāpiri 24x ki te -24x. Ka whakakore atu ngā kupu 24x me -24x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.

$$12y+8y=0$$

Tāpiri 12y ki te 8y.

$$20y=0$$

Whakawehea ngā taha e rua ki te 20.

$$y=0$$

Whakaurua te 0 mō y ki 6x-2y=0. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$6x=0$$

Whakawehea ngā taha e rua ki te 6.

$$x=0$$

Kua oti te pūnaha te whakatau.

$$x=0,y=0$$