Question

Given, $x=2y+5$ and $y=(2x-3)(x+9)$
How many ordered pairs $(x,y)$ satisfy the system of equations shown above?

• A. 0
• B. 1
• C. 2
• D. Infinitely many

Answer 1

The correct option is C 2

On putting $x=2y+5$ in second equation, we get
$y=(4y+7)(2y+14)$
$\Rightarrow 8y^2+70y+98=y$
$\Rightarrow 8y^2+69y+98=0$
Discriminant $D={69}^2-4\left(8\right)\left(98\right)=1625>0$
Hence, the equation has $2$ real roots.
Therefore, there are $2$ ordered pair.
Option C is correct.