Whakaoti i te {l}{4-y=2x?}{text{A.}2+y=2x}

$$\left. \begin{array} { l } { 4 - y = 2 x ? } \\ { \text { A. } 2 + y = 2 x } \end{array} \right.$$

Whakaoti mō y, x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$y=1$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Tangohia te 2x mai i ngā taha e rua.

$$4-y-2x=0$$

Tangohia te 4 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-y-2x=-4$$

Whakaarohia te whārite tuarua. Tangohia te 2x mai i ngā taha e rua.

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

Tangohia te 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$y-2x=-2$$

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.

$$-y-2x=-4,y-2x=-2$$

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

$$-y-2x=-4$$

Me tāpiri 2x ki ngā taha e rua o te whārite.

$$-y=2x-4$$

Whakawehea ngā taha e rua ki te -1.

$$y=-\left(2x-4\right)$$

Whakareatia -1 ki te -4+2x.

$$y=-2x+4$$

Whakakapia te -2x+4 mō te y ki tērā atu whārite, y-2x=-2.

$$-2x+4-2x=-2$$

Tāpiri -2x ki te -2x.

$$-4x+4=-2$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$-4x=-6$$

Whakawehea ngā taha e rua ki te -4.

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

Whakaurua te \frac{3}{2} mō x ki y=-2x+4. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.

$$y=-2\times \frac{3}{2}+4$$

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

$$y=-3+4$$

Tāpiri 4 ki te -3.

$$y=1$$

Kua oti te pūnaha te whakatau.

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

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Tangohia te 2x mai i ngā taha e rua.

$$4-y-2x=0$$

Tangohia te 4 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-y-2x=-4$$

Whakaarohia te whārite tuarua. Tangohia te 2x mai i ngā taha e rua.

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

Tangohia te 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$y-2x=-2$$

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

$$-y-2x=-4,y-2x=-2$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

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

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

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

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

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

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

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

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.

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

Mahia ngā tātaitanga.

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

Whakareatia ngā poukapa.

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

Mahia ngā tātaitanga.

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

Tangohia ngā huānga poukapa y me x.

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

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Tangohia te 2x mai i ngā taha e rua.

$$4-y-2x=0$$

Tangohia te 4 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-y-2x=-4$$

Whakaarohia te whārite tuarua. Tangohia te 2x mai i ngā taha e rua.

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

Tangohia te 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$y-2x=-2$$

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.

$$-y-2x=-4,y-2x=-2$$

Me tango y-2x=-2 mai i -y-2x=-4 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$-y-y-2x+2x=-4+2$$

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.

$$-y-y=-4+2$$

Tāpiri -y ki te -y.

$$-2y=-4+2$$

Tāpiri -4 ki te 2.

$$-2y=-2$$

Whakawehea ngā taha e rua ki te -2.

$$y=1$$

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

$$1-2x=-2$$

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

$$-2x=-3$$

Kua oti te pūnaha te whakatau.

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