1. **State the problem:** We are given two linear equations: $$y = 2x - 4$$ $$y = 4x - 6$$ We want to find the point where these two lines intersect. 2. **Set the equations equal:** Since both expressions equal $y$, set them equal to each other to find $x$: $$2x - 4 = 4x - 6$$ 3. **Solve for $x$:** Subtract $2x$ from both sides: $$\cancel{2x} - 4 = 4x - 6 - \cancel{2x}$$ $$-4 = 2x - 6$$ Add 6 to both sides: $$-4 + 6 = 2x - 6 + 6$$ $$2 = 2x$$ Divide both sides by 2: $$\frac{2}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ $$1 = x$$ 4. **Find $y$:** Substitute $x=1$ into one of the original equations, for example $y = 2x - 4$: $$y = 2(1) - 4 = 2 - 4 = -2$$ 5. **Final answer:** The lines intersect at the point $$(1, -2)$$ This means when $x=1$, both lines have the same $y$ value of $-2$.