Question

Question 9 (ii)
Solve the following pairs of equation
$\frac{x}{3}+\frac{y}{4}=4\frac{5x}{6}-\frac{y}{8}=4$

Answer 1

Given pair of linear equations is
$\frac{x}{3}+\frac{y}{4}=4$ and $\frac{5x}{6}-\frac{y}{8}=4$

The first equation is $\frac{x}{3}+\frac{y}{4}=4$

The LCM of 3 and 4 is 12.
On multiplying both sides by the LCM of 3 and 4, we get:
$4x+3y=\mathrm{48........}\left(i\right)$

The second equation is $\frac{5x}{6}-\frac{y}{8}=4$

The LCM of 6 and 8 is 24.
on multiplying both sides by the LCM of 6 and 8, we get
$20x-3y=\mathrm{96.......}\left(ii\right)$

Now, adding Eqs. (i) and (ii), we get
$24x=144$
$\Rightarrow x=6$
Now, adding Eqs.(i), we get
$4\times 6+3y=48$
$\Rightarrow 3y=48–24$
$\Rightarrow 3y=24\Rightarrow y=8$

Hence, the required values of x an y are 6 and 8, respectively