Whakaoti i te {l}{6x-y=-1}{6x+y=-1}

$$\left\{ \begin{array} { l } { 6 x - y = - 1 } \\ { 6 x + y = - 1 } \end{array} \right.$$

Whakaoti mō x, y

$$x=-\frac{1}{6}\approx -0.166666667$$

$$y=0$$

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.

$$6x-y=-1,6x+y=-1$$

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

$$6x-y=-1$$

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

$$6x=y-1$$

Whakawehea ngā taha e rua ki te 6.

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

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

$$x=\frac{1}{6}y-\frac{1}{6}$$

Whakakapia te \frac{-1+y}{6} mō te x ki tērā atu whārite, 6x+y=-1.

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

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

$$y-1+y=-1$$

Tāpiri y ki te y.

$$2y-1=-1$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$2y=0$$

Whakawehea ngā taha e rua ki te 2.

$$y=0$$

Whakaurua te 0 mō y ki x=\frac{1}{6}y-\frac{1}{6}. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$x=-\frac{1}{6}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{1}{6},y=0$$

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.

$$6x-y=-1,6x+y=-1$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

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

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}6&-1\\6&1\end{matrix}\right).

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

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

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

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

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

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.

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

Mahia ngā tātaitanga.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{12}&\frac{1}{12}\\-\frac{1}{2}&\frac{1}{2}\end{matrix}\right)\left(\begin{matrix}-1\\-1\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{12}\left(-1\right)+\frac{1}{12}\left(-1\right)\\-\frac{1}{2}\left(-1\right)+\frac{1}{2}\left(-1\right)\end{matrix}\right)$$

Mahia ngā tātaitanga.

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

Tangohia ngā huānga poukapa x me y.

$$x=-\frac{1}{6},y=0$$

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.

$$6x-y=-1,6x+y=-1$$

Me tango 6x+y=-1 mai i 6x-y=-1 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$6x-6x-y-y=-1+1$$

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.

$$-y-y=-1+1$$

Tāpiri -y ki te -y.

$$-2y=-1+1$$

Tāpiri -1 ki te 1.

$$-2y=0$$

Whakawehea ngā taha e rua ki te -2.

$$y=0$$

Whakaurua te 0 mō y ki 6x+y=-1. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$6x=-1$$

Whakawehea ngā taha e rua ki te 6.

$$x=-\frac{1}{6}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{1}{6},y=0$$