Whakaoti i te {l}{x-1=-3/2(y+2)}{x+y-2=0}

$$\left\{ \begin{array} { l } { x - 1 = - \frac { 3 } { 2 } ( y + 2 ) } \\ { x + y - 2 = 0 } \end{array} \right.$$

Whakaoti mō x, y

$$x=10$$

$$y=-8$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{3}{2} ki te y+2.

$$x-1=-\frac{3}{2}y-3$$

Me tāpiri te \frac{3}{2}y ki ngā taha e rua.

$$x-1+\frac{3}{2}y=-3$$

Me tāpiri te 1 ki ngā taha e rua.

$$x+\frac{3}{2}y=-3+1$$

Tāpirihia te -3 ki te 1, ka -2.

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

Whakaarohia te whārite tuarua. Me tāpiri te 2 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x+y=2$$

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.

$$x+\frac{3}{2}y=-2,x+y=2$$

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

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

Me tango \frac{3y}{2} mai i ngā taha e rua o te whārite.

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

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

$$-\frac{3}{2}y-2+y=2$$

Tāpiri -\frac{3y}{2} ki te y.

$$-\frac{1}{2}y-2=2$$

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

$$-\frac{1}{2}y=4$$

Me whakarea ngā taha e rua ki te -2.

$$y=-8$$

Whakaurua te -8 mō y ki x=-\frac{3}{2}y-2. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō x hāngai tonu.

$$x=-\frac{3}{2}\left(-8\right)-2$$

Whakareatia -\frac{3}{2} ki te -8.

$$x=12-2$$

Tāpiri -2 ki te 12.

$$x=10$$

Kua oti te pūnaha te whakatau.

$$x=10,y=-8$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{3}{2} ki te y+2.

$$x-1=-\frac{3}{2}y-3$$

Me tāpiri te \frac{3}{2}y ki ngā taha e rua.

$$x-1+\frac{3}{2}y=-3$$

Me tāpiri te 1 ki ngā taha e rua.

$$x+\frac{3}{2}y=-3+1$$

Tāpirihia te -3 ki te 1, ka -2.

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

Whakaarohia te whārite tuarua. Me tāpiri te 2 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x+y=2$$

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

$$x+\frac{3}{2}y=-2,x+y=2$$

Tuhia ngā whārite ki te tikanga tātai poukapa.

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

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

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

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

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

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

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

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.

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

Mahia ngā tātaitanga.

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

Whakareatia ngā poukapa.

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

Mahia ngā tātaitanga.

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}10\\-8\end{matrix}\right)$$

Tangohia ngā huānga poukapa x me y.

$$x=10,y=-8$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{3}{2} ki te y+2.

$$x-1=-\frac{3}{2}y-3$$

Me tāpiri te \frac{3}{2}y ki ngā taha e rua.

$$x-1+\frac{3}{2}y=-3$$

Me tāpiri te 1 ki ngā taha e rua.

$$x+\frac{3}{2}y=-3+1$$

Tāpirihia te -3 ki te 1, ka -2.

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

Whakaarohia te whārite tuarua. Me tāpiri te 2 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x+y=2$$

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.

$$x+\frac{3}{2}y=-2,x+y=2$$

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

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

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

$$\frac{3}{2}y-y=-2-2$$

Tāpiri \frac{3y}{2} ki te -y.

$$\frac{1}{2}y=-2-2$$

Tāpiri -2 ki te -2.

$$\frac{1}{2}y=-4$$

Me whakarea ngā taha e rua ki te 2.

$$y=-8$$

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

$$x-8=2$$

Me tāpiri 8 ki ngā taha e rua o te whārite.

$$x=10$$

Kua oti te pūnaha te whakatau.

$$x=10,y=-8$$