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

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 = $\frac{1}{2}$

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