Question

Find the value x and y using substitution method:
$2x-5y=9$ and $5x+6y=8$

• A. $94$ and $199$
• B. $\frac{94}{43}$ and $\frac{199}{215}$
• C. $\frac{-94}{43}$ and $\frac{199}{215}$
• D. $\frac{-94}{43}$ and $\frac{-199}{215}$

Answer 1

The correct option is B $\frac{94}{43}$ and $\frac{199}{215}$

$2x-5y=9$ -----(1)
$5x+6y=8$ -----(2)
from equation (1)
$2x-5y=9$
$y=\frac{2x-9}{5}$
substitute the balue of $y$ in equation (2)
$5x+6\left(\frac{2x-9}{5}\right)=8$
$25x+18x-54=40$
$43x=40+54$
$43x=94$
$x=\frac{94}{43}$
Substitute the value of $x$ in equation (1)
$2\left(\frac{94}{43}\right)-5y=9$
$188-215y=387$
$188-387=215y$
$y=\frac{199}{215}$
Therefore solution is $x=\frac{94}{43}$ and $y=\frac{199}{215}$