1. **State the problem:** Solve the system of equations $$\begin{cases} x - 2y = 0 \\ y = 2x - 3 \end{cases}$$ 2. **Use substitution:** From the first equation, express $x$ in terms of $y$: $$x = 2y$$ 3. **Substitute into the second equation:** Replace $x$ with $2y$: $$y = 2(2y) - 3$$ 4. **Simplify:** $$y = 4y - 3$$ 5. **Isolate $y$:** $$y - 4y = -3$$ $$\cancel{y} - 4\cancel{y} = -3$$ $$-3y = -3$$ 6. **Divide both sides by $-3$:** $$\frac{-3y}{\cancel{-3}} = \frac{-3}{\cancel{-3}}$$ $$y = 1$$ 7. **Find $x$ using $x = 2y$:** $$x = 2(1) = 2$$ 8. **Final solution:** $$\boxed{(x, y) = (2, 1)}$$ This means the two lines intersect at the point $(2,1)$. --- "slug": "linear system", "subject": "algebra", "desmos": { "latex": "x - 2y = 0, y = 2x - 3", "features": { "intercepts": true, "extrema": true } }, "q_count": 4