Question

Solve:
$2x-9y=9,5x+2y=27$

• A. $x=\frac{261}{49},y=\frac{9}{49}$
• B. $x=\frac{9}{49},y=\frac{261}{49}$
• C. $x=\frac{19}{49},y=\frac{26}{49}$
• D. $x=\frac{49}{261},y=\frac{49}{149}$

Answer 1

The correct option is A $x=\frac{261}{49},y=\frac{9}{49}$

Given,
$2x-9y=9...\left(1\right)5x+2y=27...\left(2\right)$

Multiplying (1) by 5 and (2) by 2, we get
$10x-45y=45...\left(3\right)$
$10x+4y=54...\left(4\right)$
$\left(4\right)-\left(3\right)⟹49y=9⟹y=\frac{9}{49}$

Now,
$\text{From equation}\left(1\right)$

$x=\frac{9+9y}{2}=\frac{9+9\left(\frac{9}{49}\right)}{2}=\frac{261}{49}$

$\therefore x=\frac{261}{49},y=\frac{9}{49}$