1. **State the problem:** We need to find the number of weeks $x$ when Plant A and Plant B have the same height $y$. 2. **Write the equations:** Plant A: $y = 1.8x + 3.1$ Plant B: $y = 2.3x + 1.9$ 3. **Set the heights equal to find the intersection:** $$1.8x + 3.1 = 2.3x + 1.9$$ 4. **Solve for $x$:** Subtract $1.8x$ from both sides: $$\cancel{1.8x} + 3.1 = 2.3x - \cancel{1.8x} + 1.9 \implies 3.1 = 0.5x + 1.9$$ Subtract $1.9$ from both sides: $$3.1 - 1.9 = 0.5x + \cancel{1.9} - \cancel{1.9} \implies 1.2 = 0.5x$$ Divide both sides by $0.5$: $$\frac{1.2}{\cancel{0.5}} = \frac{0.5x}{\cancel{0.5}} \implies 2.4 = x$$ 5. **Interpret the result:** It will take approximately $2.4$ weeks for both plants to reach the same height. **Final answer:** $\boxed{2.4}$ weeks