Whakaoti i te {l}{2x+y-6=0}{2x+2y=0}

$$\left\{ \begin{array} { l } { 2 x + y - 6 = 0 } \\ { 2 x + 2 y = 0 } \end{array} \right.$$

Whakaoti mō x, y

$$x=6$$

$$y=-6$$

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.

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

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

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

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$2x+y=6$$

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

$$2x=-y+6$$

Whakawehea ngā taha e rua ki te 2.

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

Whakareatia \frac{1}{2} ki te -y+6.

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

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

$$2\left(-\frac{1}{2}y+3\right)+2y=0$$

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

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

Tāpiri -y ki te 2y.

$$y+6=0$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$y=-6$$

Whakaurua te -6 mō y ki x=-\frac{1}{2}y+3. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$x=-\frac{1}{2}\left(-6\right)+3$$

Whakareatia -\frac{1}{2} ki te -6.

$$x=3+3$$

Tāpiri 3 ki te 3.

$$x=6$$

Kua oti te pūnaha te whakatau.

$$x=6,y=-6$$

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.

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

Tuhia ngā whārite ki te tikanga tātai poukapa.

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

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

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

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

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

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

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

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.

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

Mahia ngā tātaitanga.

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

Whakareatia ngā poukapa.

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

Tangohia ngā huānga poukapa x me y.

$$x=6,y=-6$$

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.

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

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

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

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

$$y-2y-6=0$$

Tāpiri y ki te -2y.

$$-y-6=0$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$-y=6$$

Whakawehea ngā taha e rua ki te -1.

$$y=-6$$

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

$$2x+2\left(-6\right)=0$$

Whakareatia 2 ki te -6.

$$2x-12=0$$

Me tāpiri 12 ki ngā taha e rua o te whārite.

$$2x=12$$

Whakawehea ngā taha e rua ki te 2.

$$x=6$$

Kua oti te pūnaha te whakatau.

$$x=6,y=-6$$