\left\{ \begin{array} { l } { x + y = 20 } \\ { y = 7 x } \end{array} \right.
Whakaoti mō x, y
x = \frac{5}{2} = 2\frac{1}{2} = 2.5
y = \frac{35}{2} = 17\frac{1}{2} = 17.5
Graph
Tohaina
Kua tāruatia ki te papatopenga
y-7x=0
Whakaarohia te whārite tuarua. Tangohia te 7x mai i ngā taha e rua.
x+y=20,-7x+y=0
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+y=20
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=-y+20
Me tango y mai i ngā taha e rua o te whārite.
-7\left(-y+20\right)+y=0
Whakakapia te -y+20 mō te x ki tērā atu whārite, -7x+y=0.
7y-140+y=0
Whakareatia -7 ki te -y+20.
8y-140=0
Tāpiri 7y ki te y.
8y=140
Me tāpiri 140 ki ngā taha e rua o te whārite.
y=\frac{35}{2}
Whakawehea ngā taha e rua ki te 8.
x=-\frac{35}{2}+20
Whakaurua te \frac{35}{2} mō y ki x=-y+20. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.
x=\frac{5}{2}
Tāpiri 20 ki te -\frac{35}{2}.
x=\frac{5}{2},y=\frac{35}{2}
Kua oti te pūnaha te whakatau.
y-7x=0
Whakaarohia te whārite tuarua. Tangohia te 7x mai i ngā taha e rua.
x+y=20,-7x+y=0
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\\-7&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}20\\0\end{matrix}\right)
Tuhia ngā whārite ki te tikanga tātai poukapa.
inverse(\left(\begin{matrix}1&1\\-7&1\end{matrix}\right))\left(\begin{matrix}1&1\\-7&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\-7&1\end{matrix}\right))\left(\begin{matrix}20\\0\end{matrix}\right)
Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}1&1\\-7&1\end{matrix}\right).
\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\-7&1\end{matrix}\right))\left(\begin{matrix}20\\0\end{matrix}\right)
Ko te hua o tētahi poukapa me te kōaro ko te poukapa tuakiri.
\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\-7&1\end{matrix}\right))\left(\begin{matrix}20\\0\end{matrix}\right)
Whakareatia ngā poukapa kei te taha mauī o te tohu ōrite.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{1-\left(-7\right)}&-\frac{1}{1-\left(-7\right)}\\-\frac{-7}{1-\left(-7\right)}&\frac{1}{1-\left(-7\right)}\end{matrix}\right)\left(\begin{matrix}20\\0\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}{8}&-\frac{1}{8}\\\frac{7}{8}&\frac{1}{8}\end{matrix}\right)\left(\begin{matrix}20\\0\end{matrix}\right)
Mahia ngā tātaitanga.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{8}\times 20\\\frac{7}{8}\times 20\end{matrix}\right)
Whakareatia ngā poukapa.
\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{5}{2}\\\frac{35}{2}\end{matrix}\right)
Mahia ngā tātaitanga.
x=\frac{5}{2},y=\frac{35}{2}
Tangohia ngā huānga poukapa x me y.
y-7x=0
Whakaarohia te whārite tuarua. Tangohia te 7x mai i ngā taha e rua.
x+y=20,-7x+y=0
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+7x+y-y=20
Me tango -7x+y=0 mai i x+y=20 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.
x+7x=20
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.
8x=20
Tāpiri x ki te 7x.
x=\frac{5}{2}
Whakawehea ngā taha e rua ki te 8.
-7\times \frac{5}{2}+y=0
Whakaurua te \frac{5}{2} mō x ki -7x+y=0. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.
-\frac{35}{2}+y=0
Whakareatia -7 ki te \frac{5}{2}.
y=\frac{35}{2}
Me tāpiri \frac{35}{2} ki ngā taha e rua o te whārite.
x=\frac{5}{2},y=\frac{35}{2}
Kua oti te pūnaha te whakatau.
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