Question

In the system of equations $8x=5y$ and $13x=8y+1$, the values of, x and y which satisfy the given equations are

• A. 8 and 5
• B. 3 and 4
• C. 10 and 16
• D. 5 and 8

Answer 1

The correct option is D 5 and 8

$\because 8x=5y\Rightarrow x=\frac{5y}{8}$ ......(i)
and $13x=8y+1\Rightarrow x=\frac{8y+1}{13}$ .....(ii)
From equations (i) and (ii),
$\frac{5y}{8}=\frac{8y+1}{13}\Rightarrow 65y=64y+8\Rightarrow y=8$
On substituting this value of y in equation (i), we get
$x=\frac{5\times 8}{8}=5$
$\therefore x=5$ and $y=8$