1. **State the problem:** Solve the system of equations: $$y = |x|$$ $$y = 2|x| + 3$$ 2. **Set the equations equal to find intersection points:** Since both equal $y$, set: $$|x| = 2|x| + 3$$ 3. **Solve for $|x|$:** $$|x| = 2|x| + 3$$ Subtract $2|x|$ from both sides: $$|x| - 2|x| = 3$$ $$\cancel{|x|} - 2\cancel{|x|} = 3$$ $$- |x| = 3$$ Multiply both sides by $-1$: $$|x| = -3$$ 4. **Analyze the result:** The absolute value $|x|$ cannot be negative, so $|x| = -3$ has no solution. 5. **Conclusion:** There is no $x$ that satisfies both equations simultaneously. **Final answer:** No solution.