Question

Solve:

$\frac{3x-2}{3y+7}=\frac{5x-1}{5y+16};\frac{3x-15}{x-9}=\frac{6y-5}{2y+3}$

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

Answer 1

Answer: (B)

$x=3,y=2$

$\Rightarrow \frac{3x-2}{3y+7}=\frac{5x-1}{5y+16}$
$\Rightarrow 15xy-10y+48x-32=15xy+35x-3y-7$
$\Rightarrow 13x-7y=\mathrm{25.........}eq1$
$\Rightarrow \frac{3x-15}{x-9}=\frac{6y-5}{2y+3}$
$\Rightarrow 6xy-30y+9x-45=6xy-54y-5x+45$
$\Rightarrow 14x+24y=\mathrm{90.......}eq2$
Multiply eq1 by 24 and eq2 by 7
$\Rightarrow 312x-168y=\mathrm{600.......}eq3$
$\Rightarrow 98x+168y=\mathrm{630.......}eq4$
Add eq3 and eq4
$\Rightarrow 410x=1230$
$\Rightarrow x=3$
Put x=3 in eq 1
$\Rightarrow 13\times 3-7y=25$
$\Rightarrow -7y=-14$
$\Rightarrow y=2$
Hence, x=3 and y=2