Solve the following system of equations:

$x\ +\ \frac{y}{2}\ =\ 4$
$2y\ +\ \frac{x}{3}\ =\ 5$

Given:

The given system of equations is:

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

$2y\ +\ \frac{x}{3}\ =\ 5$

To do:

We have to solve the given system of equations.

Solution:

The given system of equations can be written as,

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

$\Rightarrow \frac{2x+y}{2}=4$

$\Rightarrow 2x+y=2(4)$

$\Rightarrow 2x+y=8$---(i)

$2y+\frac{x}{3}=5$

$\Rightarrow \frac{3(2y)+x}{3}=5$

$\Rightarrow x+6y=3(5)$

$\Rightarrow x=15-6y$----(ii)

Substitute $x=15-6y$ in equation (i), we get,

$2(15-6y)+y=8$

$30-12y+y=8$ 

$-11y=8-30$

$-11y=-22$

$y=\frac{-22}{-11}$

$y=2$

Substituting the value of $y=2$ in equation (ii), we get,

$x=15-6(2)$

$x=15-12$

$x=3$

Therefore, the solution of the given system of equations is $x=3$ and $y=2$.

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Updated on: 10-Oct-2022

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