Question

Solve: $\frac{34}{3x+4y}+\frac{15}{3x-2y}=5$ and $\frac{25}{3x-2y}-\frac{8.50}{3x+4y}=4.5$

• A. $x=1;y=4$
• B. $x=3;y=2$
• C. $x=5;y=8$
• D. $x=7;y=6$

Answer 1

Answer: (B)

$x=3;y=2$

On putting $\frac{1}{3x+4y}=X$ and $\frac{1}{3x-2y}=Y$ in given equations, we get

$34X+15Y=5$ ...(i)

$25Y-\frac{17}{2}X=4.5\Rightarrow -17X+50Y=9$ ...(ii)

On multiplying (i) by 1 and (ii) by 2 and adding, we get

$34X+15Y=5$

$\underset{–}{-34X+100Y=18}$
$115Y=23$

$\therefore Y=\frac{23}{115}=\frac{1}{5}$

On putting $Y=\frac{1}{5}$ in (i), we get
$34X+15\times \frac{1}{5}=5\Rightarrow 34X=2\Rightarrow X=\frac{1}{17}$

$\therefore 3x+4y=17$ ...(iii)
$3x-2y=5$ ...(iv)

On subtracting (iv) from (iii), we get
$6y=12\Rightarrow y=2$

On putting $y=2$ in (iv), we get
$3x-4=5\Rightarrow x=\frac{9}{3}=3$

Therefore, $x=3,y=2$