# Solve the following system of equations: $x\ +\ 2y\ =\ \frac{3}{2}$ $2x\ +\ y\ =\ \frac{3}{2}$

Given:

The given system of equations is:

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

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

To do:

We have to solve the given system of equations.

Solution:

The given system of equations can be written as,

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

$\Rightarrow 2(x+2y)=3$   (On cross multiplication)

$\Rightarrow 2x+4y=3$---(i)

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

$\Rightarrow 2(2x+y)=3$     (On cross multiplication)

$\Rightarrow 4x+2y=3$

$\Rightarrow x=\frac{3-2y}{4}$----(ii)

Substitute $x=\frac{3-2y}{4}$ in equation (i), we get,

$2(\frac{3-2y}{4})+4y=3$

$\frac{3-2y}{2}+4y=3$

Multiplying by $2$ on both sides, we get,

$2(\frac{3-2y}{2})+2(4y)=2(3)$

$3-2y+8y=6$

$6y=6-3$

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

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

Substituting the value of $y=\frac{1}{2}$ in equation (ii), we get,

$x=\frac{3-2(\frac{1}{2})}{4}$

$x=\frac{3-1}{4}$

$x=\frac{2}{4}$

$x=\frac{1}{2}$

Therefore, the solution of the given system of equations is $x=\frac{1}{2}$ and $y=\frac{1}{2}$.

Updated on: 10-Oct-2022

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