1. **State the problem:** Find the point of intersection of the two lines given by the equations: $$y = 10x - 6$$ $$y = x - 2$$ We need to find the values of $x$ and $y$ where these two lines meet. 2. **Set the equations equal:** Since both expressions equal $y$, set them equal to each other: $$10x - 6 = x - 2$$ 3. **Solve for $x$:** Subtract $x$ from both sides: $$10x - 6 - x = x - 2 - x$$ $$9x - 6 = -2$$ Add 6 to both sides: $$9x - 6 + 6 = -2 + 6$$ $$9x = 4$$ Divide both sides by 9: $$x = \frac{4}{9}$$ Intermediate step showing cancellation: $$x = \frac{\cancel{4}}{\cancel{9}} \text{ (no common factors to cancel, so } x=\frac{4}{9})$$ 4. **Find $y$:** Substitute $x = \frac{4}{9}$ into one of the original equations, for example $y = x - 2$: $$y = \frac{4}{9} - 2 = \frac{4}{9} - \frac{18}{9} = -\frac{14}{9}$$ 5. **Round to the nearest hundredth:** $$x \approx 0.44$$ $$y \approx -1.56$$ **Final answer:** $$(x, y) = (0.44, -1.56)$$