Whakaoti i te {l}{3/8(2w+3)+5/4w=3/4(4w+1)}{3/4(y+7)+frac{1}{2}(3y-5)=frac{9}{4}(2y-1)}

$$\left. \begin{array} { l } { \frac { 3 } { 8 } ( 2 w + 3 ) + \frac { 5 } { 4 } w = \frac { 3 } { 4 } ( 4 w + 1 ) } \\ { \frac { 3 } { 4 } ( y + 7 ) + \frac { 1 } { 2 } ( 3 y - 5 ) = \frac { 9 } { 4 } ( 2 y - 1 ) } \end{array} \right.$$

Whakaoti mō w, y

$$y = \frac{20}{9} = 2\frac{2}{9} \approx 2.222222222$$

$$w=\frac{3}{8}=0.375$$

Ngā Upane Otinga

Whakaarohia te whārite tuatahi. Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{8} ki te 2w+3.

$$\frac{3}{4}w+\frac{9}{8}+\frac{5}{4}w=\frac{3}{4}\left(4w+1\right)$$

Pahekotia te \frac{3}{4}w me \frac{5}{4}w, ka 2w.

$$2w+\frac{9}{8}=\frac{3}{4}\left(4w+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{4} ki te 4w+1.

$$2w+\frac{9}{8}=3w+\frac{3}{4}$$

Tangohia te 3w mai i ngā taha e rua.

$$2w+\frac{9}{8}-3w=\frac{3}{4}$$

Pahekotia te 2w me -3w, ka -w.

$$-w+\frac{9}{8}=\frac{3}{4}$$

Tangohia te \frac{9}{8} mai i ngā taha e rua.

$$-w=\frac{3}{4}-\frac{9}{8}$$

Tangohia te \frac{9}{8} i te \frac{3}{4}, ka -\frac{3}{8}.

$$-w=-\frac{3}{8}$$

Whakawehea ngā taha e rua ki te -1.

$$w=\frac{-\frac{3}{8}}{-1}$$

Tuhia te \frac{-\frac{3}{8}}{-1} hei hautanga kotahi.

$$w=\frac{-3}{8\left(-1\right)}$$

Whakareatia te 8 ki te -1, ka -8.

$$w=\frac{-3}{-8}$$

Ka taea te hautanga \frac{-3}{-8} te whakamāmā ki te \frac{3}{8} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$w=\frac{3}{8}$$

Whakaarohia te whārite tuarua. Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{4} ki te y+7.

$$\frac{3}{4}y+\frac{21}{4}+\frac{1}{2}\left(3y-5\right)=\frac{9}{4}\left(2y-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te 3y-5.

$$\frac{3}{4}y+\frac{21}{4}+\frac{3}{2}y-\frac{5}{2}=\frac{9}{4}\left(2y-1\right)$$

Pahekotia te \frac{3}{4}y me \frac{3}{2}y, ka \frac{9}{4}y.

$$\frac{9}{4}y+\frac{21}{4}-\frac{5}{2}=\frac{9}{4}\left(2y-1\right)$$

Tangohia te \frac{5}{2} i te \frac{21}{4}, ka \frac{11}{4}.

$$\frac{9}{4}y+\frac{11}{4}=\frac{9}{4}\left(2y-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{9}{4} ki te 2y-1.

$$\frac{9}{4}y+\frac{11}{4}=\frac{9}{2}y-\frac{9}{4}$$

Tangohia te \frac{9}{2}y mai i ngā taha e rua.

$$\frac{9}{4}y+\frac{11}{4}-\frac{9}{2}y=-\frac{9}{4}$$

Pahekotia te \frac{9}{4}y me -\frac{9}{2}y, ka -\frac{9}{4}y.

$$-\frac{9}{4}y+\frac{11}{4}=-\frac{9}{4}$$

Tangohia te \frac{11}{4} mai i ngā taha e rua.

$$-\frac{9}{4}y=-\frac{9}{4}-\frac{11}{4}$$

Tangohia te \frac{11}{4} i te -\frac{9}{4}, ka -5.

$$-\frac{9}{4}y=-5$$

Me whakarea ngā taha e rua ki te -\frac{4}{9}, te tau utu o -\frac{9}{4}.

$$y=-5\left(-\frac{4}{9}\right)$$

Whakareatia te -5 ki te -\frac{4}{9}, ka \frac{20}{9}.

$$y=\frac{20}{9}$$

Kua oti te pūnaha te whakatau.

$$w=\frac{3}{8} y=\frac{20}{9}$$