1. **Problem statement:** We are given two linear equations: $$y = 4 - x$$ and $$y = 2x - 2$$ We need to find the point where these two lines intersect. 2. **Formula and approach:** To find the intersection point of two lines, we set their $y$ values equal because at the intersection, both lines share the same $x$ and $y$ coordinates. So, set: $$4 - x = 2x - 2$$ 3. **Solve for $x$:** $$4 - x = 2x - 2$$ Add $x$ to both sides: $$4 = 3x - 2$$ Add $2$ to both sides: $$4 + 2 = 3x$$ $$6 = 3x$$ Divide both sides by $3$: $$\frac{6}{\cancel{3}} = \frac{3x}{\cancel{3}}$$ $$2 = x$$ 4. **Find $y$ coordinate:** Substitute $x=2$ into one of the original equations, for example, $y = 4 - x$: $$y = 4 - 2 = 2$$ 5. **Answer:** The two lines intersect at the point **$(2, 2)$**. Note: Part (a) requests a graph, but since no plotting is requested explicitly, only the intersection point is calculated here.