Question

Solve following pair of equations by equating the coefficient method:

$8x=5y$
$13x=8y+1$

• A. $x=3$ and $y=1$
• B. $x=5$ and $y=8$
• C. $x=6$ and $y=2$
• D. $x=9$ and $y=-5$

Answer 1

Answer: (B)

$x=5$ and $y=8$

Rewriting the given equations, we get
$8x-5y=0$ ...(i)
$13x-8y=1$ ...(ii)
On multiplying (i) by 13 and (ii) by 8, we get
$104x-65y=0$
$\underset{–}{\underset{-}{1}04x\underset{+}{-}64y=\underset{-}{8}}$
$-y=-8$
$\therefore y=8$
On putting $y=8$ in (i), we get
$x=\frac{5y}{8}\Rightarrow x=5$
$\therefore x=5,y=8$