$y=2x$ and $y^2-xy=8$

Question

I'm stuck with this problem that my teacher gave me it's supposed to be a simulation equation but I have no clue what to do can you give me a step by step solution, thanks in advance.

Answer 1

with $y=2x$ we get in the second equation $$4x^2-2x^2=8$$

Answer 2

You are given the equation: $$y^2 - xy = \{8 : y = 2x \}$$ So just replace $y$ with $2x$: $$\begin{align} \implies 8 &= (2x)^2 - xy \\ &= 4x^2 - xy \\ &= x(4x - y) \\ &= x(4x - 2x) \\ &= 2x^2 \\ \implies x^2 &= 8/2 \\ &= 4 \\ \therefore x &= \pm\sqrt{4} \\ &= \pm 2 \\ \therefore y &= \pm 4 \end{align}$$. $$: \ = \text{ such that}$$ $$\implies \ = \text{ which implies that}$$ $$\therefore \ = \text{ therefore}$$ $$\pm \ = \text{ positive or negative (plus or minus)}$$