Whakaoti i te {l}{7x=y}{(17+1)x-9=y}

$$\left. \begin{array} { l } { 7 x = y } \\ { ( 17 + 1 ) x - 9 = y } \end{array} \right.$$

Whakaoti mō x, y

$$x=\frac{9}{11}\approx 0.818181818$$

$$y = \frac{63}{11} = 5\frac{8}{11} \approx 5.727272727$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Tangohia te y mai i ngā taha e rua.

$$7x-y=0$$

Whakaarohia te whārite tuarua. Tāpirihia te 17 ki te 1, ka 18.

$$18x-9=y$$

Tangohia te y mai i ngā taha e rua.

$$18x-9-y=0$$

Me tāpiri te 9 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$18x-y=9$$

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.

$$7x-y=0,18x-y=9$$

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

$$7x-y=0$$

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

$$7x=y$$

Whakawehea ngā taha e rua ki te 7.

$$x=\frac{1}{7}y$$

Whakakapia te \frac{y}{7} mō te x ki tērā atu whārite, 18x-y=9.

$$18\times \frac{1}{7}y-y=9$$

Whakareatia 18 ki te \frac{y}{7}.

$$\frac{18}{7}y-y=9$$

Tāpiri \frac{18y}{7} ki te -y.

$$\frac{11}{7}y=9$$

Whakawehea ngā taha e rua o te whārite ki te \frac{11}{7}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$y=\frac{63}{11}$$

Whakaurua te \frac{63}{11} mō y ki x=\frac{1}{7}y. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$x=\frac{1}{7}\times \frac{63}{11}$$

Whakareatia \frac{1}{7} ki te \frac{63}{11} 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.

$$x=\frac{9}{11}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{9}{11},y=\frac{63}{11}$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Tangohia te y mai i ngā taha e rua.

$$7x-y=0$$

Whakaarohia te whārite tuarua. Tāpirihia te 17 ki te 1, ka 18.

$$18x-9=y$$

Tangohia te y mai i ngā taha e rua.

$$18x-9-y=0$$

Me tāpiri te 9 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$18x-y=9$$

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

$$7x-y=0,18x-y=9$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

$$\left(\begin{matrix}7&-1\\18&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}0\\9\end{matrix}\right)$$

Whakarea mauī i te whārite ki te poukapa kōaro o \left(\begin{matrix}7&-1\\18&-1\end{matrix}\right).

$$inverse(\left(\begin{matrix}7&-1\\18&-1\end{matrix}\right))\left(\begin{matrix}7&-1\\18&-1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}7&-1\\18&-1\end{matrix}\right))\left(\begin{matrix}0\\9\end{matrix}\right)$$

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

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}7&-1\\18&-1\end{matrix}\right))\left(\begin{matrix}0\\9\end{matrix}\right)$$

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

$$\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}7&-1\\18&-1\end{matrix}\right))\left(\begin{matrix}0\\9\end{matrix}\right)$$

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.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{7\left(-1\right)-\left(-18\right)}&-\frac{-1}{7\left(-1\right)-\left(-18\right)}\\-\frac{18}{7\left(-1\right)-\left(-18\right)}&\frac{7}{7\left(-1\right)-\left(-18\right)}\end{matrix}\right)\left(\begin{matrix}0\\9\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{11}&\frac{1}{11}\\-\frac{18}{11}&\frac{7}{11}\end{matrix}\right)\left(\begin{matrix}0\\9\end{matrix}\right)$$

Whakareatia ngā poukapa.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{11}\times 9\\\frac{7}{11}\times 9\end{matrix}\right)$$

Mahia ngā tātaitanga.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{9}{11}\\\frac{63}{11}\end{matrix}\right)$$

Tangohia ngā huānga poukapa x me y.

$$x=\frac{9}{11},y=\frac{63}{11}$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Tangohia te y mai i ngā taha e rua.

$$7x-y=0$$

Whakaarohia te whārite tuarua. Tāpirihia te 17 ki te 1, ka 18.

$$18x-9=y$$

Tangohia te y mai i ngā taha e rua.

$$18x-9-y=0$$

Me tāpiri te 9 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$18x-y=9$$

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.

$$7x-y=0,18x-y=9$$

Me tango 18x-y=9 mai i 7x-y=0 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

$$7x-18x-y+y=-9$$

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.

$$7x-18x=-9$$

Tāpiri 7x ki te -18x.

$$-11x=-9$$

Whakawehea ngā taha e rua ki te -11.

$$x=\frac{9}{11}$$

Whakaurua te \frac{9}{11} mō x ki 18x-y=9. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.

$$18\times \frac{9}{11}-y=9$$

Whakareatia 18 ki te \frac{9}{11}.

$$\frac{162}{11}-y=9$$

Me tango \frac{162}{11} mai i ngā taha e rua o te whārite.

$$-y=-\frac{63}{11}$$

Whakawehea ngā taha e rua ki te -1.

$$y=\frac{63}{11}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{9}{11},y=\frac{63}{11}$$