Whakaoti i te {l}{x-3/5+x-4/7=6-2x-1/35}{y=x+5}{z=2x+6}{a=y}{b=z}{text{Solvefor}c,dtext{where}}{c=a}{d=b}

$$\left. \begin{array} { l } { \frac{x - 3}{5} + \frac{x - 4}{7} = 6 - \frac{2 x - 1}{35} }\\ { y = x + 5 }\\ { z = 2 x + 6 }\\ { a = y }\\ { b = z }\\ { \text{Solve for } c,d \text{ where} } \\ { c = a }\\ { d = b } \end{array} \right.$$

Whakaoti mō x, y, z, a, b, c, d

$$c=23$$

$$d=42$$

Ngā Upane Otinga

Whakaarohia te whārite tuatahi. Me whakarea ngā taha e rua o te whārite ki te 35, arā, te tauraro pātahi he tino iti rawa te kitea o 5,7,35.

$$7\left(x-3\right)+5\left(x-4\right)=210-\left(2x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 7 ki te x-3.

$$7x-21+5\left(x-4\right)=210-\left(2x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te x-4.

$$7x-21+5x-20=210-\left(2x-1\right)$$

Pahekotia te 7x me 5x, ka 12x.

$$12x-21-20=210-\left(2x-1\right)$$

Tangohia te 20 i te -21, ka -41.

$$12x-41=210-\left(2x-1\right)$$

Hei kimi i te tauaro o 2x-1, kimihia te tauaro o ia taurangi.

$$12x-41=210-2x+1$$

Tāpirihia te 210 ki te 1, ka 211.

$$12x-41=211-2x$$

Me tāpiri te 2x ki ngā taha e rua.

$$12x-41+2x=211$$

Pahekotia te 12x me 2x, ka 14x.

$$14x-41=211$$

Me tāpiri te 41 ki ngā taha e rua.

$$14x=211+41$$

Tāpirihia te 211 ki te 41, ka 252.

$$14x=252$$

Whakawehea ngā taha e rua ki te 14.

$$x=\frac{252}{14}$$

Whakawehea te 252 ki te 14, kia riro ko 18.

$$x=18$$

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

$$y=18+5$$

Tāpirihia te 18 ki te 5, ka 23.

$$y=23$$

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

$$z=2\times 18+6$$

Whakareatia te 2 ki te 18, ka 36.

$$z=36+6$$

Tāpirihia te 36 ki te 6, ka 42.

$$z=42$$

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

$$a=23$$

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

$$b=42$$

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

$$c=23$$

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

$$d=42$$

Kua oti te pūnaha te whakatau.

$$x=18 y=23 z=42 a=23 b=42 c=23 d=42$$