Solve the following pairs of equations:
$ \frac{x}{3}+\frac{y}{4}=4 $
$ \frac{5 x}{6}-\frac{y}{8}=4 $

AcademicMathematicsNCERTClass 10

Given: 

The given pair of equations is:

\( \frac{x}{3}+\frac{y}{4}=4 \)

\( \frac{5 x}{6}-\frac{y}{8}=4 \)

To do: 

We have to solve the given pair of equations.

Solution: 

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

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

$4x+3y=12(4)$

$3y=48-4x$......(i)

$\frac{5x}{6}-\frac{y}{8}=4$

$\Rightarrow \frac{4(5x)-3(y)}{24}=4$

$20x-3y=24(4)$

$20x=96+3y$

$20x=96+48-4x$          [From (i)]

$20x+4x=144$

$24x=144$

$x=\frac{144}{24}$

$x=6$

This implies,

$y=\frac{48-4(6)}{3}$

$y=\frac{24}{3}$

$y=8$

Hence, the solution of the given pair of equations is $x=6$ and $y=8$.

raja
Updated on 10-Oct-2022 13:27:15

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