Whakaoti i te y=-3/2x;quady=-2-1/2x

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

Whakaoti mō y, x

$$x=2$$

$$y=-3$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Me tāpiri te \frac{3}{2}x ki ngā taha e rua.

$$y+\frac{3}{2}x=0$$

Whakaarohia te whārite tuarua. Me tāpiri te \frac{1}{2}x ki ngā taha e rua.

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

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.

$$y+\frac{3}{2}x=0,y+\frac{1}{2}x=-2$$

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

$$y+\frac{3}{2}x=0$$

Me tango \frac{3x}{2} mai i ngā taha e rua o te whārite.

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

Whakakapia te -\frac{3x}{2} mō te y ki tērā atu whārite, y+\frac{1}{2}x=-2.

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

Tāpiri -\frac{3x}{2} ki te \frac{x}{2}.

$$-x=-2$$

Whakawehea ngā taha e rua ki te -1.

$$x=2$$

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

$$y=-\frac{3}{2}\times 2$$

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

$$y=-3$$

Kua oti te pūnaha te whakatau.

$$y=-3,x=2$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Me tāpiri te \frac{3}{2}x ki ngā taha e rua.

$$y+\frac{3}{2}x=0$$

Whakaarohia te whārite tuarua. Me tāpiri te \frac{1}{2}x ki ngā taha e rua.

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

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

$$y+\frac{3}{2}x=0,y+\frac{1}{2}x=-2$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}1&\frac{3}{2}\\1&\frac{1}{2}\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}0\\-2\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&\frac{3}{2}\\1&\frac{1}{2}\end{matrix}\right).

$$inverse(\left(\begin{matrix}1&\frac{3}{2}\\1&\frac{1}{2}\end{matrix}\right))\left(\begin{matrix}1&\frac{3}{2}\\1&\frac{1}{2}\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&\frac{3}{2}\\1&\frac{1}{2}\end{matrix}\right))\left(\begin{matrix}0\\-2\end{matrix}\right)$$

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

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&\frac{3}{2}\\1&\frac{1}{2}\end{matrix}\right))\left(\begin{matrix}0\\-2\end{matrix}\right)$$

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

$$\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&\frac{3}{2}\\1&\frac{1}{2}\end{matrix}\right))\left(\begin{matrix}0\\-2\end{matrix}\right)$$

Mō te poukapa 2\times 2 \left(\begin{matrix}a&b\\c&d\end{matrix}\right), ko te poukapa kōaro ko \left(\begin{matrix}\frac{d}{ad-bc}&\frac{-b}{ad-bc}\\\frac{-c}{ad-bc}&\frac{a}{ad-bc}\end{matrix}\right), kia tuhia anō ai te whārite poukapa hei rapanga whakarea poukapa.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{\frac{1}{2}}{\frac{1}{2}-\frac{3}{2}}&-\frac{\frac{3}{2}}{\frac{1}{2}-\frac{3}{2}}\\-\frac{1}{\frac{1}{2}-\frac{3}{2}}&\frac{1}{\frac{1}{2}-\frac{3}{2}}\end{matrix}\right)\left(\begin{matrix}0\\-2\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{2}&\frac{3}{2}\\1&-1\end{matrix}\right)\left(\begin{matrix}0\\-2\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{3}{2}\left(-2\right)\\-\left(-2\right)\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-3\\2\end{matrix}\right)$$

Tangohia ngā huānga poukapa y me x.

$$y=-3,x=2$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Me tāpiri te \frac{3}{2}x ki ngā taha e rua.

$$y+\frac{3}{2}x=0$$

Whakaarohia te whārite tuarua. Me tāpiri te \frac{1}{2}x ki ngā taha e rua.

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

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.

$$y+\frac{3}{2}x=0,y+\frac{1}{2}x=-2$$

Me tango y+\frac{1}{2}x=-2 mai i y+\frac{3}{2}x=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

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

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.

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

Tāpiri \frac{3x}{2} ki te -\frac{x}{2}.

$$x=2$$

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

$$y+\frac{1}{2}\times 2=-2$$

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

$$y+1=-2$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$y=-3$$

Kua oti te pūnaha te whakatau.

$$y=-3,x=2$$