Whakaoti i te y=2x/5text{y}5x+y+5=0

$$y = 2 x / 5 \text { y } 5 x + y + 5 = 0$$

Whakaoti mō y, x

$$x=-\frac{25}{27}\approx -0.925925926$$

$$y=-\frac{10}{27}\approx -0.37037037$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Tangohia te \frac{2x}{5} mai i ngā taha e rua.

$$y-\frac{2x}{5}=0$$

Whakareatia ngā taha e rua o te whārite ki te 5.

$$5y-2x=0$$

Whakaarohia te whārite tuarua. Tangohia te 5 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$5x+y=-5$$

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.

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

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

$$5y-2x=0$$

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

$$5y=2x$$

Whakawehea ngā taha e rua ki te 5.

$$y=\frac{1}{5}\times 2x$$

Whakareatia \frac{1}{5} ki te 2x.

$$y=\frac{2}{5}x$$

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

$$\frac{2}{5}x+5x=-5$$

Tāpiri \frac{2x}{5} ki te 5x.

$$\frac{27}{5}x=-5$$

Whakawehea ngā taha e rua o te whārite ki te \frac{27}{5}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$x=-\frac{25}{27}$$

Whakaurua te -\frac{25}{27} mō x ki y=\frac{2}{5}x. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.

$$y=\frac{2}{5}\left(-\frac{25}{27}\right)$$

Whakareatia \frac{2}{5} ki te -\frac{25}{27} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$y=-\frac{10}{27}$$

Kua oti te pūnaha te whakatau.

$$y=-\frac{10}{27},x=-\frac{25}{27}$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Tangohia te \frac{2x}{5} mai i ngā taha e rua.

$$y-\frac{2x}{5}=0$$

Whakareatia ngā taha e rua o te whārite ki te 5.

$$5y-2x=0$$

Whakaarohia te whārite tuarua. Tangohia te 5 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$5x+y=-5$$

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

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

Tuhia ngā whārite ki te tikanga tātai poukapa.

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

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}5&-2\\1&5\end{matrix}\right).

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

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

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

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

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

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.

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

Mahia ngā tātaitanga.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{5}{27}&\frac{2}{27}\\-\frac{1}{27}&\frac{5}{27}\end{matrix}\right)\left(\begin{matrix}0\\-5\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{2}{27}\left(-5\right)\\\frac{5}{27}\left(-5\right)\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{10}{27}\\-\frac{25}{27}\end{matrix}\right)$$

Tangohia ngā huānga poukapa y me x.

$$y=-\frac{10}{27},x=-\frac{25}{27}$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Tangohia te \frac{2x}{5} mai i ngā taha e rua.

$$y-\frac{2x}{5}=0$$

Whakareatia ngā taha e rua o te whārite ki te 5.

$$5y-2x=0$$

Whakaarohia te whārite tuarua. Tangohia te 5 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$5x+y=-5$$

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.

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

Kia ōrite ai a 5y me y, 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 5.

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

Whakarūnātia.

$$5y-2x=0,5y+25x=-25$$

Me tango 5y+25x=-25 mai i 5y-2x=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$5y-5y-2x-25x=25$$

Tāpiri 5y ki te -5y. Ka whakakore atu ngā kupu 5y me -5y, ka toe he whārite me tētahi taurangi kotahi ka taea te whakaoti.

$$-2x-25x=25$$

Tāpiri -2x ki te -25x.

$$-27x=25$$

Whakawehea ngā taha e rua ki te -27.

$$x=-\frac{25}{27}$$

Whakaurua te -\frac{25}{27} mō x ki y+5x=-5. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.

$$y+5\left(-\frac{25}{27}\right)=-5$$

Whakareatia 5 ki te -\frac{25}{27}.

$$y-\frac{125}{27}=-5$$

Me tāpiri \frac{125}{27} ki ngā taha e rua o te whārite.

$$y=-\frac{10}{27}$$

Kua oti te pūnaha te whakatau.

$$y=-\frac{10}{27},x=-\frac{25}{27}$$