1. **State the problem:** We need to find the coordinate pair $(x,y)$ that satisfies both equations simultaneously: $$y = 2x - 3$$ $$y = -x + 3$$ 2. **Set the equations equal to each other:** Since both expressions equal $y$, we can set them equal: $$2x - 3 = -x + 3$$ 3. **Solve for $x$:** Add $x$ to both sides: $$2x + x - 3 = 3$$ Simplify: $$3x - 3 = 3$$ Add 3 to both sides: $$3x - \cancel{3} + \cancel{3} = 3 + 3$$ $$3x = 6$$ Divide both sides by 3: $$\frac{3x}{\cancel{3}} = \frac{6}{\cancel{3}}$$ $$x = 2$$ 4. **Find $y$ by substituting $x=2$ into one of the original equations:** Using $y = 2x - 3$: $$y = 2(2) - 3 = 4 - 3 = 1$$ 5. **Solution:** The coordinate pair that solves the system is: $$(2, 1)$$ This means the two lines intersect at the point $(2,1)$ on the Cartesian plane.