Whakaoti i te {l}{x+3x-9/5=4-5x-12/3}{y=3+3x}{z=5x-2}{a=y}{b=z}{text{Solvefor}c,dtext{where}}{c=a}{d=b}

$$\left. \begin{array} { l } { x + \frac{3 x - 9}{5} = 4 - \frac{5 x - 12}{3} }\\ { y = 3 + 3 x }\\ { z = 5 x - 2 }\\ { a = y }\\ { b = z }\\ { \text{Solve for } c,d \text{ where} } \\ { c = a }\\ { d = b } \end{array} \right.$$

Whakaoti mō x, y, z, a, b, c, d

$$c=12$$

$$d=13$$

Ngā Upane Otinga

Whakaarohia te whārite tuatahi. Me whakarea ngā taha e rua o te whārite ki te 15, arā, te tauraro pātahi he tino iti rawa te kitea o 5,3.

$$15x+3\left(3x-9\right)=60-5\left(5x-12\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 3x-9.

$$15x+9x-27=60-5\left(5x-12\right)$$

Pahekotia te 15x me 9x, ka 24x.

$$24x-27=60-5\left(5x-12\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -5 ki te 5x-12.

$$24x-27=60-25x+60$$

Tāpirihia te 60 ki te 60, ka 120.

$$24x-27=120-25x$$

Me tāpiri te 25x ki ngā taha e rua.

$$24x-27+25x=120$$

Pahekotia te 24x me 25x, ka 49x.

$$49x-27=120$$

Me tāpiri te 27 ki ngā taha e rua.

$$49x=120+27$$

Tāpirihia te 120 ki te 27, ka 147.

$$49x=147$$

Whakawehea ngā taha e rua ki te 49.

$$x=\frac{147}{49}$$

Whakawehea te 147 ki te 49, kia riro ko 3.

$$x=3$$

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

$$y=3+3\times 3$$

Whakareatia te 3 ki te 3, ka 9.

$$y=3+9$$

Tāpirihia te 3 ki te 9, ka 12.

$$y=12$$

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

$$z=5\times 3-2$$

Whakareatia te 5 ki te 3, ka 15.

$$z=15-2$$

Tangohia te 2 i te 15, ka 13.

$$z=13$$

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

$$a=12$$

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

$$b=13$$

Whakaarohia te whārite (6). Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$c=12$$

Whakaarohia te whārite (7). Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$d=13$$

Kua oti te pūnaha te whakatau.

$$x=3 y=12 z=13 a=12 b=13 c=12 d=13$$