Whakaoti i te {l}{x=y/2}{y=x-5}

$$\left. \begin{array} { l } { x = y / 2 } \\ { y = x - 5 } \end{array} \right.$$

Whakaoti mō x, y

$$x=-5$$

$$y=-10$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Tangohia te \frac{y}{2} mai i ngā taha e rua.

$$x-\frac{y}{2}=0$$

Whakareatia ngā taha e rua o te whārite ki te 2.

$$2x-y=0$$

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

$$y-x=-5$$

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.

$$2x-y=0,-x+y=-5$$

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

$$2x-y=0$$

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

$$2x=y$$

Whakawehea ngā taha e rua ki te 2.

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

Whakakapia te \frac{y}{2} mō te x ki tērā atu whārite, -x+y=-5.

$$-\frac{1}{2}y+y=-5$$

Tāpiri -\frac{y}{2} ki te y.

$$\frac{1}{2}y=-5$$

Me whakarea ngā taha e rua ki te 2.

$$y=-10$$

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

$$x=\frac{1}{2}\left(-10\right)$$

Whakareatia \frac{1}{2} ki te -10.

$$x=-5$$

Kua oti te pūnaha te whakatau.

$$x=-5,y=-10$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Tangohia te \frac{y}{2} mai i ngā taha e rua.

$$x-\frac{y}{2}=0$$

Whakareatia ngā taha e rua o te whārite ki te 2.

$$2x-y=0$$

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

$$y-x=-5$$

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

$$2x-y=0,-x+y=-5$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

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

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

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

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

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

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

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

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.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{2-\left(-\left(-1\right)\right)}&-\frac{-1}{2-\left(-\left(-1\right)\right)}\\-\frac{-1}{2-\left(-\left(-1\right)\right)}&\frac{2}{2-\left(-\left(-1\right)\right)}\end{matrix}\right)\left(\begin{matrix}0\\-5\end{matrix}\right)$$

Mahia ngā tātaitanga.

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

Whakareatia ngā poukapa.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-5\\2\left(-5\right)\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-5\\-10\end{matrix}\right)$$

Tangohia ngā huānga poukapa x me y.

$$x=-5,y=-10$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Tangohia te \frac{y}{2} mai i ngā taha e rua.

$$x-\frac{y}{2}=0$$

Whakareatia ngā taha e rua o te whārite ki te 2.

$$2x-y=0$$

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

$$y-x=-5$$

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.

$$2x-y=0,-x+y=-5$$

Kia ōrite ai a 2x 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 2.

$$-2x-\left(-y\right)=0,2\left(-1\right)x+2y=2\left(-5\right)$$

Whakarūnātia.

$$-2x+y=0,-2x+2y=-10$$

Me tango -2x+2y=-10 mai i -2x+y=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$-2x+2x+y-2y=10$$

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.

$$y-2y=10$$

Tāpiri y ki te -2y.

$$-y=10$$

Whakawehea ngā taha e rua ki te -1.

$$y=-10$$

Whakaurua te -10 mō y ki -x+y=-5. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$-x-10=-5$$

Me tāpiri 10 ki ngā taha e rua o te whārite.

$$-x=5$$

Whakawehea ngā taha e rua ki te -1.

$$x=-5$$

Kua oti te pūnaha te whakatau.

$$x=-5,y=-10$$