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