Solve: x/3=y/6 and 4x/3+2y=4

Solve: x/3=y/6 and 4x/3+2y=4

$\frac{x}{3} = \frac{y}{6}$ —(i)

$\frac{4x}{3} + 2y = 4$ —(ii)

From Equation (i) we get,

$\frac{x}{3} = \frac{y}{6}$

$\Rightarrow 6{\mathrm{x}} = 3{\mathrm{y}}$

$\Rightarrow {\mathrm{x}} = \frac{3{\mathrm{y}}}{6}$

$\Rightarrow {\mathrm{x}} = \frac{{\mathrm{y}}}{2}$ —(iii)

Substituting the value of x in equation (ii) we get,

$\frac{4{\mathrm{x}}}{3} + 2{\mathrm{y}} = 4$

$\Rightarrow \frac{4}{3}\left(\frac{{\mathrm{y}}}{2}\right) + 2{\mathrm{y}} = 4[\because {\mathrm{x}} = \frac{{\mathrm{y}}}{2}]$

$\Rightarrow \frac{2{\mathrm{y}}}{3} + 2{\mathrm{y}} = 4$

$\Rightarrow \frac{2{\mathrm{y}} + 6{\mathrm{y}}}{3} = 4$

$\Rightarrow 8{\mathrm{y}} = 12$

$\Rightarrow {\mathrm{y}} = \frac{12}{8}$

$\Rightarrow {\mathrm{y}} = \frac{3}{2}$

Now from (iii) we get,

${\mathrm{x}} = \frac{{\mathrm{y}}}{2}$

$\Rightarrow {\mathrm{x}} = \frac{\frac{3}{2}}{2}$

$\Rightarrow {\mathrm{x}} = \frac{3}{4}$

Therefore Required Solutions are x =$\frac{3}{4}$ and y=$\frac{3}{2}$