1. **State the problem:** We need to graph the system of equations and find the point where the two lines intersect. 2. **Write down the system:** $$y = 2x - 4$$ $$y = 4x - 6$$ 3. **Set the equations equal to find the intersection:** Since both equal $y$, set: $$2x - 4 = 4x - 6$$ 4. **Solve for $x$:** $$2x - 4 = 4x - 6$$ Subtract $2x$ from both sides: $$\cancel{2x} - 4 = \cancel{2x} + 2x - 6$$ Simplifies to: $$-4 = 2x - 6$$ Add 6 to both sides: $$-4 + 6 = 2x - 6 + 6$$ $$2 = 2x$$ Divide both sides by 2: $$\frac{2}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ $$1 = x$$ 5. **Find $y$ by substituting $x=1$ into one of the equations:** Using $y = 2x - 4$: $$y = 2(1) - 4 = 2 - 4 = -2$$ 6. **Conclusion:** The point of intersection is at: $$\boxed{(1, -2)}$$ This means the solution to the system is $x=1$, $y=-2$. 7. **Graphing notes:** - The first line has slope 2 and y-intercept -4. - The second line has slope 4 and y-intercept -6. - They intersect at the point $(1, -2)$.