Whakaoti i te {l}{2x-x=4m+2}{x-2x=5m-5}

$$\left\{ \begin{array} { l } { 2 x - x = 4 m + 2 } \\ { x - 2 x = 5 m - 5 } \end{array} \right.$$

Whakaoti mō x, m

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

$$m=\frac{1}{3}\approx 0.333333333$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Pahekotia te 2x me -x, ka x.

$$x=4m+2$$

Whakakapia te 4m+2 mō te x ki tērā atu whārite, -x-5m=-5.

$$-\left(4m+2\right)-5m=-5$$

Whakareatia -1 ki te 4m+2.

$$-4m-2-5m=-5$$

Tāpiri -4m ki te -5m.

$$-9m-2=-5$$

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

$$-9m=-3$$

Whakawehea ngā taha e rua ki te -9.

$$m=\frac{1}{3}$$

Whakaurua te \frac{1}{3} mō m ki x=4m+2. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$x=4\times \frac{1}{3}+2$$

Whakareatia 4 ki te \frac{1}{3}.

$$x=\frac{4}{3}+2$$

Tāpiri 2 ki te \frac{4}{3}.

$$x=\frac{10}{3}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{10}{3},m=\frac{1}{3}$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Pahekotia te 2x me -x, ka x.

$$x=4m+2$$

Tangohia te 4m mai i ngā taha e rua.

$$x-4m=2$$

Whakaarohia te whārite tuarua. Pahekotia te x me -2x, ka -x.

$$-x=5m-5$$

Tangohia te 5m mai i ngā taha e rua.

$$-x-5m=-5$$

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

$$x-4m=2,-x-5m=-5$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}1&-4\\-1&-5\end{matrix}\right)\left(\begin{matrix}x\\m\end{matrix}\right)=\left(\begin{matrix}2\\-5\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&-4\\-1&-5\end{matrix}\right).

$$inverse(\left(\begin{matrix}1&-4\\-1&-5\end{matrix}\right))\left(\begin{matrix}1&-4\\-1&-5\end{matrix}\right)\left(\begin{matrix}x\\m\end{matrix}\right)=inverse(\left(\begin{matrix}1&-4\\-1&-5\end{matrix}\right))\left(\begin{matrix}2\\-5\end{matrix}\right)$$

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

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\m\end{matrix}\right)=inverse(\left(\begin{matrix}1&-4\\-1&-5\end{matrix}\right))\left(\begin{matrix}2\\-5\end{matrix}\right)$$

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

$$\left(\begin{matrix}x\\m\end{matrix}\right)=inverse(\left(\begin{matrix}1&-4\\-1&-5\end{matrix}\right))\left(\begin{matrix}2\\-5\end{matrix}\right)$$

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.

$$\left(\begin{matrix}x\\m\end{matrix}\right)=\left(\begin{matrix}-\frac{5}{-5-\left(-4\left(-1\right)\right)}&-\frac{-4}{-5-\left(-4\left(-1\right)\right)}\\-\frac{-1}{-5-\left(-4\left(-1\right)\right)}&\frac{1}{-5-\left(-4\left(-1\right)\right)}\end{matrix}\right)\left(\begin{matrix}2\\-5\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}x\\m\end{matrix}\right)=\left(\begin{matrix}\frac{5}{9}&-\frac{4}{9}\\-\frac{1}{9}&-\frac{1}{9}\end{matrix}\right)\left(\begin{matrix}2\\-5\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}x\\m\end{matrix}\right)=\left(\begin{matrix}\frac{5}{9}\times 2-\frac{4}{9}\left(-5\right)\\-\frac{1}{9}\times 2-\frac{1}{9}\left(-5\right)\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}x\\m\end{matrix}\right)=\left(\begin{matrix}\frac{10}{3}\\\frac{1}{3}\end{matrix}\right)$$

Tangohia ngā huānga poukapa x me m.

$$x=\frac{10}{3},m=\frac{1}{3}$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Pahekotia te 2x me -x, ka x.

$$x=4m+2$$

Tangohia te 4m mai i ngā taha e rua.

$$x-4m=2$$

Whakaarohia te whārite tuarua. Pahekotia te x me -2x, ka -x.

$$-x=5m-5$$

Tangohia te 5m mai i ngā taha e rua.

$$-x-5m=-5$$

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.

$$x-4m=2,-x-5m=-5$$

Kia ōrite ai a x me -x, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te -1 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 1.

$$-x-\left(-4m\right)=-2,-x-5m=-5$$

Whakarūnātia.

$$-x+4m=-2,-x-5m=-5$$

Me tango -x-5m=-5 mai i -x+4m=-2 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$-x+x+4m+5m=-2+5$$

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

$$4m+5m=-2+5$$

Tāpiri 4m ki te 5m.

$$9m=-2+5$$

Tāpiri -2 ki te 5.

$$9m=3$$

Whakawehea ngā taha e rua ki te 9.

$$m=\frac{1}{3}$$

Whakaurua te \frac{1}{3} mō m ki -x-5m=-5. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$-x-5\times \frac{1}{3}=-5$$

Whakareatia -5 ki te \frac{1}{3}.

$$-x-\frac{5}{3}=-5$$

Me tāpiri \frac{5}{3} ki ngā taha e rua o te whārite.

$$-x=-\frac{10}{3}$$

Whakawehea ngā taha e rua ki te -1.

$$x=\frac{10}{3}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{10}{3},m=\frac{1}{3}$$