Whakaoti i te x/2+y/3+z/4=x+y+z/5

$$\frac { x } { 2 } + \frac { y } { 3 } + \frac { z } { 4 } = \frac { x + y + z } { 5 }$$

Whakaoti mō x

$$x=-\frac{z}{6}-\frac{4y}{9}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 60, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3,4,5.

$$30x+20y+15z=12\left(x+y+z\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 12 ki te x+y+z.

$$30x+20y+15z=12x+12y+12z$$

Tangohia te 12x mai i ngā taha e rua.

$$30x+20y+15z-12x=12y+12z$$

Pahekotia te 30x me -12x, ka 18x.

$$18x+20y+15z=12y+12z$$

Tangohia te 20y mai i ngā taha e rua.

$$18x+15z=12y+12z-20y$$

Pahekotia te 12y me -20y, ka -8y.

$$18x+15z=-8y+12z$$

Tangohia te 15z mai i ngā taha e rua.

$$18x=-8y+12z-15z$$

Pahekotia te 12z me -15z, ka -3z.

$$18x=-8y-3z$$

Whakawehea ngā taha e rua ki te 18.

$$\frac{18x}{18}=\frac{-8y-3z}{18}$$

Mā te whakawehe ki te 18 ka wetekia te whakareanga ki te 18.

$$x=\frac{-8y-3z}{18}$$

Whakawehe -8y-3z ki te 18.

$$x=-\frac{z}{6}-\frac{4y}{9}$$

Whakaoti mō y

$$y=-\frac{3z}{8}-\frac{9x}{4}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 60, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3,4,5.

$$30x+20y+15z=12\left(x+y+z\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 12 ki te x+y+z.

$$30x+20y+15z=12x+12y+12z$$

Tangohia te 12y mai i ngā taha e rua.

$$30x+20y+15z-12y=12x+12z$$

Pahekotia te 20y me -12y, ka 8y.

$$30x+8y+15z=12x+12z$$

Tangohia te 30x mai i ngā taha e rua.

$$8y+15z=12x+12z-30x$$

Pahekotia te 12x me -30x, ka -18x.

$$8y+15z=-18x+12z$$

Tangohia te 15z mai i ngā taha e rua.

$$8y=-18x+12z-15z$$

Pahekotia te 12z me -15z, ka -3z.

$$8y=-18x-3z$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8y}{8}=\frac{-18x-3z}{8}$$

Mā te whakawehe ki te 8 ka wetekia te whakareanga ki te 8.

$$y=\frac{-18x-3z}{8}$$

Whakawehe -18x-3z ki te 8.

$$y=-\frac{3z}{8}-\frac{9x}{4}$$