• No products in the cart.

# Real solutions (Tomato subjective 71)

problem: Consider the following simultaneous equations in x and y :
$${\displaystyle{4x + y + axy = a}}$$
$${\displaystyle{x – 2y -xy^2 = 0}}$$
where $${\displaystyle{a}}$$ is a real constant. Show that these equations admit real solutions in x and y.

solution: $${\displaystyle{4x + y + axy = a}}$$          …  (i)
$${\displaystyle{x – 2y -xy^2 = 0}}$$           … (ii)
$${\displaystyle{x – 2y -xy^2 = 0}}$$
$${\Rightarrow}$$ $${\displaystyle{x = {\frac{2y}{1-y^2}}}}$$
$${\displaystyle{x + y + axy = a}}$$