Solve: x+2y=3/2 and 2x+y=3/2
$x + 2y = \frac{3}{2}$ —(i)
$2x+y=\frac{3}{2}$ —(ii)
Multiplying Equation (ii) by 2 we get,
$4x + 2y = 2 \times \frac{3}{2}$
$\Rightarrow 4x + 2y = 3$ —(iii)
Subtracting Equation (i) from (iii) we get,
(4x + 2y)- (x+2y) = 3-$\frac{3}{2}$
⟹ 4x + 2y -x -2y = $\frac{6 – 3}{2}$
⟹ 3x = $\frac{3}{2}$
⟹ x =$\frac{1}{2}$
From Equation (i) we get,
$x + 2y = \frac{3}{2}$
$\Rightarrow \frac{1}{2} + 2y = \frac{3}{2}$ [As, x=$\frac{1}{2}$]
$\Rightarrow 2y = \frac{3}{2} – \frac{1}{2}$
$\Rightarrow 2y = \frac{3 – 1}{2}$
$\Rightarrow 2y = \frac{2}{2}$
$\Rightarrow 2y = 1$
$\Rightarrow y = \frac{1}{2}$
Required Solutions are x =$\frac{1}{2}$ , y = $\frac{1}{2}$