Solving a Simultaneous Equation. I'm in no way unfamiliar with these sorts of equations and have had plenty of practice with them, however I'm going insane over a question I feel I should be able to easily answer algebraically but am stuck on. This is the question: Solve for $x$ & $y$. 1: $2^x = y$ 2: $3-x = y$ Sorry for boring you with such a mundane question, but its driving me mental. Thanks for any help. (Sorry if there are any formatting issues, I'm new to this StackExchange).

Since both RHS = y is equivalent to the single equation. $$ 2^x = 3-x. $$

If you haven't found a way to solve this algebraically, I don't blame yourself. There is no way to 'solve for x' in algebra. This is a transcendental function and must be solved graphically.

If you graph $2^x$ and $3-x$, you'll see they intersect once. By inspection $x =1$ is a solution, so that's the one real solution.

(additionally there are complex solutions in terms of the Lambert W-function)