Question

Solve the following pair of equations :

$\frac{3}{5}x-\frac{2}{3}y+1=0$
$\frac{1}{3}y+\frac{2}{5}x=4$

• A. $x=2;y=-1$
• B. $x=5;y=6$
• C. $x=7;y=-4$
• D. $x=0;y=5$

Answer 1

The correct option is B $x=5;y=6$

Given, $\frac{3}{5}x-\frac{2}{3}y+1=0\Rightarrow 9x-10y=-15$ ...(i)

$\frac{1}{3}y+\frac{2}{5}x=4\Rightarrow 6x+5y=60$ ...(ii)

On multiplying (i) by $2$ and (ii) by $3$ and subtracting, we get

$18x-20y=-30$
$\underset{–}{\underset{-}{1}8x\underset{-}{+}15y=\underset{+}{-}180}$
$-35y=-210$
$\therefore y=6$
On putting $y=6$ in (ii), we get
$6x+30=60$

$\Rightarrow x=5$

Therefore, the numbers be $x=5,y=6$.