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

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

Whakaoti mō y, x

$$x=-4$$

$$y=-7$$

Ngā Upane e Whakamahi ana i te Whakakapinga

Whakaarohia te whārite tuatahi. Tangohia te \frac{3}{2}x mai i ngā taha e rua.

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

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.

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

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

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

Me tāpiri \frac{3x}{2} ki ngā taha e rua o te whārite.

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

Whakakapia te \frac{3x}{2}-1 mō te y ki tērā atu whārite, y-x=-3.

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

Tāpiri \frac{3x}{2} ki te -x.

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

Me tāpiri 1 ki ngā taha e rua o te whārite.

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

Me whakarea ngā taha e rua ki te 2.

$$x=-4$$

Whakaurua te -4 mō x ki y=\frac{3}{2}x-1. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.

$$y=\frac{3}{2}\left(-4\right)-1$$

Whakareatia \frac{3}{2} ki te -4.

$$y=-6-1$$

Tāpiri -1 ki te -6.

$$y=-7$$

Kua oti te pūnaha te whakatau.

$$y=-7,x=-4$$

Ngā Upane e Whakamahi ana i Ngā Poukapa

Whakaarohia te whārite tuatahi. Tangohia te \frac{3}{2}x mai i ngā taha e rua.

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

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

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

Tuhia ngā whārite ki te tikanga tātai poukapa.

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

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

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

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

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

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

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

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.

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

Mahia ngā tātaitanga.

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

Whakareatia ngā poukapa.

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

Mahia ngā tātaitanga.

$$\left(\begin{matrix}y\\x\end{matrix}\right)=\left(\begin{matrix}-7\\-4\end{matrix}\right)$$

Tangohia ngā huānga poukapa y me x.

$$y=-7,x=-4$$

Ngā Upane e Whakamahi i te Tangohanga

Whakaarohia te whārite tuatahi. Tangohia te \frac{3}{2}x mai i ngā taha e rua.

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

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.

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

Me tango y-x=-3 mai i y-\frac{3}{2}x=-1 mā te tango i ngā kīanga tau ōrite i ia taha o te tohu ōrite.

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

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.

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

Tāpiri -\frac{3x}{2} ki te x.

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

Tāpiri -1 ki te 3.

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

Me whakarea ngā taha e rua ki te -2.

$$x=-4$$

Whakaurua te -4 mō x ki y-x=-3. I te mea kotahi anake te taurangi kei te whārite i puta, ka taea e koe te whakaoti mō y hāngai tonu.

$$y-\left(-4\right)=-3$$

Whakareatia -1 ki te -4.

$$y+4=-3$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$y=-7$$

Kua oti te pūnaha te whakatau.

$$y=-7,x=-4$$