Whakaoti i te {l}{x/14+x/18=1}{x+y/2+3x-5y/4=2}

$$\left. \begin{array} { l } { \frac { x } { 14 } + \frac { x } { 18 } = 1 } \\ { \frac { x + y } { 2 } + \frac { 3 x - 5 y } { 4 } = 2 } \end{array} \right.$$

Whakaoti mō x, y

$$x = \frac{63}{8} = 7\frac{7}{8} = 7.875$$

$$y = \frac{251}{24} = 10\frac{11}{24} \approx 10.458333333$$

Ngā Upane Otinga

Whakaarohia te whārite tuatahi. Me whakarea ngā taha e rua o te whārite ki te 126, arā, te tauraro pātahi he tino iti rawa te kitea o 14,18.

$$9x+7x=126$$

Pahekotia te 9x me 7x, ka 16x.

$$16x=126$$

Whakawehea ngā taha e rua ki te 16.

$$x=\frac{126}{16}$$

Whakahekea te hautanga \frac{126}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{63}{8}$$

Whakaarohia te whārite tuarua. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$\frac{\frac{63}{8}+y}{2}+\frac{3\times \frac{63}{8}-5y}{4}=2$$

Me whakarea ngā taha e rua o te whārite ki te 4, arā, te tauraro pātahi he tino iti rawa te kitea o 2,4.

$$2\left(\frac{63}{8}+y\right)+3\times \frac{63}{8}-5y=8$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te \frac{63}{8}+y.

$$\frac{63}{4}+2y+3\times \frac{63}{8}-5y=8$$

Whakareatia te 3 ki te \frac{63}{8}, ka \frac{189}{8}.

$$\frac{63}{4}+2y+\frac{189}{8}-5y=8$$

Tāpirihia te \frac{63}{4} ki te \frac{189}{8}, ka \frac{315}{8}.

$$\frac{315}{8}+2y-5y=8$$

Pahekotia te 2y me -5y, ka -3y.

$$\frac{315}{8}-3y=8$$

Tangohia te \frac{315}{8} mai i ngā taha e rua.

$$-3y=8-\frac{315}{8}$$

Tangohia te \frac{315}{8} i te 8, ka -\frac{251}{8}.

$$-3y=-\frac{251}{8}$$

Whakawehea ngā taha e rua ki te -3.

$$y=\frac{-\frac{251}{8}}{-3}$$

Tuhia te \frac{-\frac{251}{8}}{-3} hei hautanga kotahi.

$$y=\frac{-251}{8\left(-3\right)}$$

Whakareatia te 8 ki te -3, ka -24.

$$y=\frac{-251}{-24}$$

Ka taea te hautanga \frac{-251}{-24} te whakamāmā ki te \frac{251}{24} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$y=\frac{251}{24}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{63}{8} y=\frac{251}{24}$$