1. **State the problem:** Solve the system of linear equations: $$\text{I. } y = 2x + 3$$ $$\text{II. } 3x + 2y = 13$$ Find the values of $x$ and $y$ that satisfy both equations simultaneously. 2. **Use substitution method:** Since equation I is already solved for $y$, substitute $y = 2x + 3$ into equation II. $$3x + 2(2x + 3) = 13$$ 3. **Simplify the equation:** $$3x + 4x + 6 = 13$$ $$7x + 6 = 13$$ 4. **Isolate $x$:** $$7x = 13 - 6$$ $$7x = 7$$ 5. **Solve for $x$:** $$x = \frac{7}{7}$$ $$x = 1$$ 6. **Substitute $x=1$ back into equation I to find $y$:** $$y = 2(1) + 3$$ $$y = 2 + 3$$ $$y = 5$$ 7. **Final answer:** $$x = 1, \quad y = 5$$ This means the two lines intersect at the point $(1, 5)$.