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

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

Whakaoti mō y, x

$$x=1$$

$$y=-5$$

Ngā Upane e Whakamahi ana i te Whakakapinga

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

$$y-x=-6$$

Whakaarohia te whārite tuarua. Me tāpiri te 6x ki ngā taha e rua.

$$y+6x=1$$

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.

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

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

$$y-x=-6$$

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

$$y=x-6$$

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

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

Tāpiri x ki te 6x.

$$7x-6=1$$

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

$$7x=7$$

Whakawehea ngā taha e rua ki te 7.

$$x=1$$

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

$$y=1-6$$

Tāpiri -6 ki te 1.

$$y=-5$$

Kua oti te pūnaha te whakatau.

$$y=-5,x=1$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

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

$$y-x=-6$$

Whakaarohia te whārite tuarua. Me tāpiri te 6x ki ngā taha e rua.

$$y+6x=1$$

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

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

Tuhia ngā whārite ki te tikanga tātai poukapa.

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

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

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

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

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

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

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

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.

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

Mahia ngā tātaitanga.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{6}{7}&\frac{1}{7}\\-\frac{1}{7}&\frac{1}{7}\end{matrix}\right)\left(\begin{matrix}-6\\1\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{6}{7}\left(-6\right)+\frac{1}{7}\\-\frac{1}{7}\left(-6\right)+\frac{1}{7}\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-5\\1\end{matrix}\right)$$

Tangohia ngā huānga poukapa y me x.

$$y=-5,x=1$$

Ngā Upane e Whakamahi i te Tangohanga

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

$$y-x=-6$$

Whakaarohia te whārite tuarua. Me tāpiri te 6x ki ngā taha e rua.

$$y+6x=1$$

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.

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

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

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

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

$$-x-6x=-6-1$$

Tāpiri -x ki te -6x.

$$-7x=-6-1$$

Tāpiri -6 ki te -1.

$$-7x=-7$$

Whakawehea ngā taha e rua ki te -7.

$$x=1$$

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

$$y+6=1$$

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

$$y=-5$$

Kua oti te pūnaha te whakatau.

$$y=-5,x=1$$