Whakaoti mō y, x
x=-6
y=4
Graph
Tohaina
Kua tāruatia ki te papatopenga
2+y+x=0
Whakaarohia te whārite tuatahi. Me tāpiri te x ki ngā taha e rua.
y+x=-2
Tangohia te 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.
-10+y-x=0
Whakaarohia te whārite tuarua. Tangohia te x mai i ngā taha e rua.
y-x=10
Me tāpiri te 10 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.
y+x=-2,y-x=10
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+x=-2
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=-x-2
Me tango x mai i ngā taha e rua o te whārite.
-x-2-x=10
Whakakapia te -x-2 mō te y ki tērā atu whārite, y-x=10.
-2x-2=10
Tāpiri -x ki te -x.
-2x=12
Me tāpiri 2 ki ngā taha e rua o te whārite.
x=-6
Whakawehea ngā taha e rua ki te -2.
y=-\left(-6\right)-2
Whakaurua te -6 mō x ki y=-x-2. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
y=6-2
Whakareatia -1 ki te -6.
y=4
Tāpiri -2 ki te 6.
y=4,x=-6
Kua oti te pūnaha te whakatau.
2+y+x=0
Whakaarohia te whārite tuatahi. Me tāpiri te x ki ngā taha e rua.
y+x=-2
Tangohia te 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.
-10+y-x=0
Whakaarohia te whārite tuarua. Tangohia te x mai i ngā taha e rua.
y-x=10
Me tāpiri te 10 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.
y+x=-2,y-x=10
Tuhia ngā whārite ki te tānga ngahuru ka whakamahi i ngā poukapa hei whakaoti i te pūnaha o ngā whārite.
\left(\begin{matrix}1&1\\1&-1\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-2\\10\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}1&1\\1&-1\end{matrix}\right))\left(\begin{matrix}1&1\\1&-1\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\1&-1\end{matrix}\right))\left(\begin{matrix}-2\\10\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&1\\1&-1\end{matrix}\right).
\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\1&-1\end{matrix}\right))\left(\begin{matrix}-2\\10\end{matrix}\right)
Ko te hua o tētahi poukapa me te kōaro ko te poukapa tuakiri.
\left(\begin{matrix}y\\x\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\1&-1\end{matrix}\right))\left(\begin{matrix}-2\\10\end{matrix}\right)
Whakareatia ngā poukapa kei te taha mauī o te tohu ōrite.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{-1-1}&-\frac{1}{-1-1}\\-\frac{1}{-1-1}&\frac{1}{-1-1}\end{matrix}\right)\left(\begin{matrix}-2\\10\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{1}{2}&\frac{1}{2}\\\frac{1}{2}&-\frac{1}{2}\end{matrix}\right)\left(\begin{matrix}-2\\10\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}\frac{1}{2}\left(-2\right)+\frac{1}{2}\times 10\\\frac{1}{2}\left(-2\right)-\frac{1}{2}\times 10\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}4\\-6\end{matrix}\right)
Mahia ngā tātaitanga.
y=4,x=-6
Tangohia ngā huānga poukapa y me x.
2+y+x=0
Whakaarohia te whārite tuatahi. Me tāpiri te x ki ngā taha e rua.
y+x=-2
Tangohia te 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.
-10+y-x=0
Whakaarohia te whārite tuarua. Tangohia te x mai i ngā taha e rua.
y-x=10
Me tāpiri te 10 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.
y+x=-2,y-x=10
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-y+x+x=-2-10
Me tango y-x=10 mai i y+x=-2 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
x+x=-2-10
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.
2x=-2-10
Tāpiri x ki te x.
2x=-12
Tāpiri -2 ki te -10.
x=-6
Whakawehea ngā taha e rua ki te 2.
y-\left(-6\right)=10
Whakaurua te -6 mō x ki y-x=10. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
y+6=10
Whakareatia -1 ki te -6.
y=4
Me tango 6 mai i ngā taha e rua o te whārite.
y=4,x=-6
Kua oti te pūnaha te whakatau.
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