1. **Problem:** Determine the solution to the system of linear equations given by: $$\text{Line A: } y = x - 2$$ $$\text{Line B: } y = -2x + 4$$ Find the point where these two lines intersect. 2. **Formula and rules:** To find the intersection point of two lines, set their equations equal to each other because at the intersection point, both lines have the same $x$ and $y$ values. 3. **Set the equations equal:** $$x - 2 = -2x + 4$$ 4. **Solve for $x$:** Add $2x$ to both sides: $$x + 2x - 2 = -2x + 2x + 4$$ $$3x - 2 = 4$$ Add 2 to both sides: $$3x - 2 + 2 = 4 + 2$$ $$3x = 6$$ Divide both sides by 3: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{6}{3}$$ $$x = 2$$ 5. **Find $y$ by substituting $x=2$ into one of the original equations:** Using Line A: $$y = 2 - 2 = 0$$ 6. **Solution:** The lines intersect at the point **$(2, 0)$**. This means the system has exactly one solution at this point. **Final answer:** (2, 0)