1. The problem is to solve the system of equations: $$y = |x|$$ $$y = 2|x| + 3$$ 2. To find the solution, set the two expressions for $y$ equal to each other: $$|x| = 2|x| + 3$$ 3. Rearrange the equation to isolate terms: $$|x| - 2|x| = 3$$ $$\cancel{|x|} - 2\cancel{|x|} = 3$$ $$- |x| = 3$$ 4. Multiply both sides by $-1$ to solve for $|x|$: $$|x| = -3$$ 5. Since the absolute value $|x|$ cannot be negative, there is no real solution to this equation. 6. Therefore, the system has no solution. Final answer: No solution.