1. **State the problem:** Solve the system of linear equations by equating the values of $y$: $$y = 3x + 2$$ $$y = 2x + 3$$ 2. **Use the method of equating values of $y$:** Since both expressions equal $y$, set them equal to each other: $$3x + 2 = 2x + 3$$ 3. **Solve for $x$:** Subtract $2x$ from both sides: $$3x + 2 - \cancel{2x} = \cancel{2x} + 3 - 2x$$ which simplifies to: $$x + 2 = 3$$ Subtract 2 from both sides: $$x + 2 - 2 = 3 - 2$$ $$x = 1$$ 4. **Find $y$ by substituting $x=1$ into one of the original equations:** Using $y = 3x + 2$: $$y = 3(1) + 2 = 3 + 2 = 5$$ 5. **Final answer:** The solution to the system is: $$(x, y) = (1, 5)$$ This means the two lines intersect at the point $(1, 5)$ on the Cartesian plane.