1. **State the problem:** We are given two linear equations: $$y = \frac{2}{3}x - 1$$ and $$y = -x + 4$$ We need to find the point where these two lines intersect. 2. **Set the equations equal to find the intersection:** Since both expressions equal $y$, set them equal to each other: $$\frac{2}{3}x - 1 = -x + 4$$ 3. **Solve for $x$:** Add $x$ to both sides: $$\frac{2}{3}x + x - 1 = 4$$ Rewrite $x$ as $\frac{3}{3}x$ to combine like terms: $$\frac{2}{3}x + \frac{3}{3}x - 1 = 4$$ $$\left(\frac{2}{3} + \frac{3}{3}\right)x - 1 = 4$$ $$\frac{5}{3}x - 1 = 4$$ Add 1 to both sides: $$\frac{5}{3}x = 5$$ 4. **Isolate $x$ by dividing both sides by $\frac{5}{3}$:** $$x = 5 \div \frac{5}{3}$$ Show cancellation: $$x = 5 \times \cancel{\frac{3}{5}} = 3$$ 5. **Find $y$ by substituting $x=3$ into one of the original equations:** Using $y = -x + 4$: $$y = -3 + 4 = 1$$ 6. **Final answer:** The lines intersect at the point $$(3, 1)$$