Whakaoti i te {c}{x=m+3}{3x=2m-1}

$$\left\{ \begin{array} { c } { x = m + 3 } \\ { 3 x = 2 m - 1 } \end{array} \right.$$

Whakaoti mō x, m

$$x=-7$$

$$m=-10$$

Ngā Upane e Whakamahi ana i te Whakakapinga

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

$$x-m=3$$

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

$$3x-2m=-1$$

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.

$$x-m=3,3x-2m=-1$$

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

$$x-m=3$$

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

$$x=m+3$$

Whakakapia te m+3 mō te x ki tērā atu whārite, 3x-2m=-1.

$$3\left(m+3\right)-2m=-1$$

Whakareatia 3 ki te m+3.

$$3m+9-2m=-1$$

Tāpiri 3m ki te -2m.

$$m+9=-1$$

Me tango 9 mai i ngā taha e rua o te whārite.

$$m=-10$$

Whakaurua te -10 mō m ki x=m+3. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$x=-10+3$$

Tāpiri 3 ki te -10.

$$x=-7$$

Kua oti te pūnaha te whakatau.

$$x=-7,m=-10$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

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

$$x-m=3$$

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

$$3x-2m=-1$$

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

$$x-m=3,3x-2m=-1$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

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

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

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

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

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

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

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

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.

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

Mahia ngā tātaitanga.

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

Whakareatia ngā poukapa.

$$\left(\begin{matrix}x\\m\end{matrix}\right)=\left(\begin{matrix}-2\times 3-1\\-3\times 3-1\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}x\\m\end{matrix}\right)=\left(\begin{matrix}-7\\-10\end{matrix}\right)$$

Tangohia ngā huānga poukapa x me m.

$$x=-7,m=-10$$

Ngā Upane e Whakamahi i te Tangohanga

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

$$x-m=3$$

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

$$3x-2m=-1$$

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.

$$x-m=3,3x-2m=-1$$

Kia ōrite ai a x me 3x, whakareatia ngā kīanga tau katoa kei ia taha o te whārite tuatahi ki te 3 me ngā kīanga tau katoa kei ia taha o te whārite tuarua ki te 1.

$$3x+3\left(-1\right)m=3\times 3,3x-2m=-1$$

Whakarūnātia.

$$3x-3m=9,3x-2m=-1$$

Me tango 3x-2m=-1 mai i 3x-3m=9 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$3x-3x-3m+2m=9+1$$

Tāpiri 3x ki te -3x. Ka whakakore atu ngā kupu 3x me -3x, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.

$$-3m+2m=9+1$$

Tāpiri -3m ki te 2m.

$$-m=9+1$$

Tāpiri 9 ki te 1.

$$-m=10$$

Whakawehea ngā taha e rua ki te -1.

$$m=-10$$

Whakaurua te -10 mō m ki 3x-2m=-1. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$3x-2\left(-10\right)=-1$$

Whakareatia -2 ki te -10.

$$3x+20=-1$$

Me tango 20 mai i ngā taha e rua o te whārite.

$$3x=-21$$

Whakawehea ngā taha e rua ki te 3.

$$x=-7$$

Kua oti te pūnaha te whakatau.

$$x=-7,m=-10$$