Whakaoti i te 2(1/2y-3x)=2y+1/2(3x-1)

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

Whakaoti mō x

$$x=\frac{1-2y}{15}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te \frac{1}{2}y-3x.

$$y-6x=2y+\frac{1}{2}\left(3x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te 3x-1.

$$y-6x=2y+\frac{3}{2}x-\frac{1}{2}$$

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

$$y-6x-\frac{3}{2}x=2y-\frac{1}{2}$$

Pahekotia te -6x me -\frac{3}{2}x, ka -\frac{15}{2}x.

$$y-\frac{15}{2}x=2y-\frac{1}{2}$$

Tangohia te y mai i ngā taha e rua.

$$-\frac{15}{2}x=2y-\frac{1}{2}-y$$

Pahekotia te 2y me -y, ka y.

$$-\frac{15}{2}x=y-\frac{1}{2}$$

Whakawehea ngā taha e rua o te whārite ki te -\frac{15}{2}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{-\frac{15}{2}x}{-\frac{15}{2}}=\frac{y-\frac{1}{2}}{-\frac{15}{2}}$$

Mā te whakawehe ki te -\frac{15}{2} ka wetekia te whakareanga ki te -\frac{15}{2}.

$$x=\frac{y-\frac{1}{2}}{-\frac{15}{2}}$$

Whakawehe y-\frac{1}{2} ki te -\frac{15}{2} mā te whakarea y-\frac{1}{2} ki te tau huripoki o -\frac{15}{2}.

$$x=\frac{1-2y}{15}$$

Whakaoti mō y

$$y=\frac{1-15x}{2}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te \frac{1}{2}y-3x.

$$y-6x=2y+\frac{1}{2}\left(3x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te 3x-1.

$$y-6x=2y+\frac{3}{2}x-\frac{1}{2}$$

Tangohia te 2y mai i ngā taha e rua.

$$y-6x-2y=\frac{3}{2}x-\frac{1}{2}$$

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

$$-y-6x=\frac{3}{2}x-\frac{1}{2}$$

Me tāpiri te 6x ki ngā taha e rua.

$$-y=\frac{3}{2}x-\frac{1}{2}+6x$$

Pahekotia te \frac{3}{2}x me 6x, ka \frac{15}{2}x.

$$-y=\frac{15}{2}x-\frac{1}{2}$$

He hanga arowhānui tō te whārite.

$$-y=\frac{15x-1}{2}$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-y}{-1}=\frac{15x-1}{-2}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$y=\frac{15x-1}{-2}$$

Whakawehe \frac{15x-1}{2} ki te -1.

$$y=\frac{1-15x}{2}$$