Solve the following systems of equations:
Question:

Solve the following systems of equations:

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

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

Solution:

The given equations are:

$x+2 y=\frac{3}{2}$ $\ldots(i)$

$2 x+y=\frac{3}{2} \ldots(i i)$

Multiply equation (ii) by 2 and subtract equation (ii) from (i) we get

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

Put the value of $x$ in equation $(i)$, we get

$\frac{1}{2}+2 y=\frac{3}{2}$

$\Rightarrow 2 y=1$

$\Rightarrow y=\frac{1}{2}$

Hence the value of $x=\frac{1}{2}$ and $y=\frac{1}{2}$