Whakaoti i te 22*16+22*8*y/x=54+y/2x*9

$$22 \times 16 + 22 \times 8 \times \frac { y } { x } = 54 + \frac { y } { 2 x } \times 9$$

Whakaoti mō x

$$x=-\frac{343y}{596}$$

$$y\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x, arā, te tauraro pātahi he tino iti rawa te kitea o x,2x.

$$22\times 16\times 2x+22\times 8\times 2y=2x\times 54+y\times 9$$

Mahia ngā whakarea.

$$352\times 2x+176\times 2y=2x\times 54+y\times 9$$

Whakareatia te 352 ki te 2, ka 704.

$$704x+176\times 2y=2x\times 54+y\times 9$$

Whakareatia te 176 ki te 2, ka 352.

$$704x+352y=2x\times 54+y\times 9$$

Whakareatia te 2 ki te 54, ka 108.

$$704x+352y=108x+y\times 9$$

Tangohia te 108x mai i ngā taha e rua.

$$704x+352y-108x=y\times 9$$

Pahekotia te 704x me -108x, ka 596x.

$$596x+352y=y\times 9$$

Tangohia te 352y mai i ngā taha e rua.

$$596x=y\times 9-352y$$

Pahekotia te y\times 9 me -352y, ka -343y.

$$596x=-343y$$

Whakawehea ngā taha e rua ki te 596.

$$\frac{596x}{596}=-\frac{343y}{596}$$

Mā te whakawehe ki te 596 ka wetekia te whakareanga ki te 596.

$$x=-\frac{343y}{596}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{343y}{596}\text{, }x\neq 0$$

Whakaoti mō y

$$y=-\frac{596x}{343}$$

$$x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$22\times 16\times 2x+22\times 8\times 2y=2x\times 54+y\times 9$$

Mahia ngā whakarea.

$$352\times 2x+176\times 2y=2x\times 54+y\times 9$$

Whakareatia te 352 ki te 2, ka 704.

$$704x+176\times 2y=2x\times 54+y\times 9$$

Whakareatia te 176 ki te 2, ka 352.

$$704x+352y=2x\times 54+y\times 9$$

Whakareatia te 2 ki te 54, ka 108.

$$704x+352y=108x+y\times 9$$

Tangohia te y\times 9 mai i ngā taha e rua.

$$704x+352y-y\times 9=108x$$

Pahekotia te 352y me -y\times 9, ka 343y.

$$704x+343y=108x$$

Tangohia te 704x mai i ngā taha e rua.

$$343y=108x-704x$$

Pahekotia te 108x me -704x, ka -596x.

$$343y=-596x$$

Whakawehea ngā taha e rua ki te 343.

$$\frac{343y}{343}=-\frac{596x}{343}$$

Mā te whakawehe ki te 343 ka wetekia te whakareanga ki te 343.

$$y=-\frac{596x}{343}$$