Solve the following system of equations:

$\frac{x}{3}\ +\ \frac{y}{4}\ =\ 11$
$\frac{5x}{6}\ −\ \frac{y}{3}\ =\ −7$

Given:

The given system of equations is:

$\frac{x}{3}\ +\ \frac{y}{4}\ =\ 11$

$\frac{5x}{6}\ −\ \frac{y}{3}\ =\ −7$

To do:

We have to solve the given system of equations.

Solution:

The given system of equations can be written as,

$\frac{x}{3}+\frac{y}{4}=11$

$\Rightarrow \frac{4(x)+3(y)}{12}=11$

$\Rightarrow 4x+3y=11(12)$   (On cross  multiplication)

$\Rightarrow 4x+3y=132$---(i)

$\frac{5x}{6}-\frac{y}{3}=-7$

$\Rightarrow \frac{5x-2(y)}{6}=-7$

$\Rightarrow 5x-2y=-7(6)$   (On cross multiplication)

$\Rightarrow 5x=2y-42$

$\Rightarrow x=\frac{2y-42}{5}$----(ii)

Substitute $x=\frac{2y-42}{5}$ in equation (i), we get,

$4(\frac{2y-42}{5})+3y=132$

$\frac{4(2y-42)}{5}+3y=132$ 

Multiplying by $5$ on both sides, we get,

$5(\frac{8y-168}{5})+5(3y)=5(132)$

$8y-168+15y=660$

$23y=660+168$

$23y=828$

$y=\frac{828}{23}$

$y=36$

Substituting the value of $y=36$ in equation (ii), we get,

$x=\frac{2(36)-42}{5}$

$x=\frac{72-42}{5}$

$x=\frac{30}{5}$

$x=6$

Therefore, the solution of the given system of equations is $x=6$ and $y=36$.

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Updated on: 10-Oct-2022

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