Whakaoti i te y=4/3x-28/3;quady=2x+8

$$y = \frac { 4 } { 3 } x - \frac { 28 } { 3 } ; \quad y = 2 x + 8$$

Whakaoti mō y, x

$$x=-26$$

$$y=-44$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Tangohia te \frac{4}{3}x mai i ngā taha e rua.

$$y-\frac{4}{3}x=-\frac{28}{3}$$

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

$$y-2x=8$$

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.

$$y-\frac{4}{3}x=-\frac{28}{3},y-2x=8$$

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

$$y-\frac{4}{3}x=-\frac{28}{3}$$

Me tāpiri \frac{4x}{3} ki ngā taha e rua o te whārite.

$$y=\frac{4}{3}x-\frac{28}{3}$$

Whakakapia te \frac{-28+4x}{3} mō te y ki tērā atu whārite, y-2x=8.

$$\frac{4}{3}x-\frac{28}{3}-2x=8$$

Tāpiri \frac{4x}{3} ki te -2x.

$$-\frac{2}{3}x-\frac{28}{3}=8$$

Me tāpiri \frac{28}{3} ki ngā taha e rua o te whārite.

$$-\frac{2}{3}x=\frac{52}{3}$$

Whakawehea ngā taha e rua o te whārite ki te -\frac{2}{3}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$x=-26$$

Whakaurua te -26 mō x ki y=\frac{4}{3}x-\frac{28}{3}. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.

$$y=\frac{4}{3}\left(-26\right)-\frac{28}{3}$$

Whakareatia \frac{4}{3} ki te -26.

$$y=\frac{-104-28}{3}$$

Tāpiri -\frac{28}{3} ki te -\frac{104}{3} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$y=-44$$

Kua oti te pūnaha te whakatau.

$$y=-44,x=-26$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Tangohia te \frac{4}{3}x mai i ngā taha e rua.

$$y-\frac{4}{3}x=-\frac{28}{3}$$

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

$$y-2x=8$$

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

$$y-\frac{4}{3}x=-\frac{28}{3},y-2x=8$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}1&-\frac{4}{3}\\1&-2\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{28}{3}\\8\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&-\frac{4}{3}\\1&-2\end{matrix}\right).

$$inverse(\left(\begin{matrix}1&-\frac{4}{3}\\1&-2\end{matrix}\right))\left(\begin{matrix}1&-\frac{4}{3}\\1&-2\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-\frac{4}{3}\\1&-2\end{matrix}\right))\left(\begin{matrix}-\frac{28}{3}\\8\end{matrix}\right)$$

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

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-\frac{4}{3}\\1&-2\end{matrix}\right))\left(\begin{matrix}-\frac{28}{3}\\8\end{matrix}\right)$$

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

$$\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&-\frac{4}{3}\\1&-2\end{matrix}\right))\left(\begin{matrix}-\frac{28}{3}\\8\end{matrix}\right)$$

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.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{2}{-2-\left(-\frac{4}{3}\right)}&-\frac{-\frac{4}{3}}{-2-\left(-\frac{4}{3}\right)}\\-\frac{1}{-2-\left(-\frac{4}{3}\right)}&\frac{1}{-2-\left(-\frac{4}{3}\right)}\end{matrix}\right)\left(\begin{matrix}-\frac{28}{3}\\8\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}3&-2\\\frac{3}{2}&-\frac{3}{2}\end{matrix}\right)\left(\begin{matrix}-\frac{28}{3}\\8\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}3\left(-\frac{28}{3}\right)-2\times 8\\\frac{3}{2}\left(-\frac{28}{3}\right)-\frac{3}{2}\times 8\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-44\\-26\end{matrix}\right)$$

Tangohia ngā huānga poukapa y me x.

$$y=-44,x=-26$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Tangohia te \frac{4}{3}x mai i ngā taha e rua.

$$y-\frac{4}{3}x=-\frac{28}{3}$$

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

$$y-2x=8$$

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.

$$y-\frac{4}{3}x=-\frac{28}{3},y-2x=8$$

Me tango y-2x=8 mai i y-\frac{4}{3}x=-\frac{28}{3} mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$y-y-\frac{4}{3}x+2x=-\frac{28}{3}-8$$

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.

$$-\frac{4}{3}x+2x=-\frac{28}{3}-8$$

Tāpiri -\frac{4x}{3} ki te 2x.

$$\frac{2}{3}x=-\frac{28}{3}-8$$

Tāpiri -\frac{28}{3} ki te -8.

$$\frac{2}{3}x=-\frac{52}{3}$$

Whakawehea ngā taha e rua o te whārite ki te \frac{2}{3}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$x=-26$$

Whakaurua te -26 mō x ki y-2x=8. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.

$$y-2\left(-26\right)=8$$

Whakareatia -2 ki te -26.

$$y+52=8$$

Me tango 52 mai i ngā taha e rua o te whārite.

$$y=-44$$

Kua oti te pūnaha te whakatau.

$$y=-44,x=-26$$