The system of equations below can be solved by substitution or elimination. I understand the official solution to this problem, which I will provide below. I'd like to understand why my initial solution failed, thank you for your assistance.
Equations:
Equation One: $$x + y = 3000$$ Equation Two: $$0.1x + 0.08y = 256$$
Correct Solution (substitution method):
$$y = -x + 3000$$ $$0.1x + 0.08(-x + 3000) = 256$$ $$x = 800$$ $$y = 2,200$$
My (incorrect) solution:
$$0.08y = 256 - 0.1x$$ $$y = \frac{256 - 0.1x}{0.08}$$ $$x + \frac{256 - 0.1x}{0.08} = 3000$$ $$x + 256 - 0.1x = 3000 \times 0.08$$ $$0.9x = -16$$ $$x = -17.78$$
So where did I go wrong?
In your fourth step, you didn't multiply $X$ by $0.08$ on the left side.