1. **State the problem:** We need to plot the graph of the system of linear equations: $$y - 2x = 5$$ $$2y + x = 0$$ 2. **Rewrite each equation in slope-intercept form $y = mx + b$ for easier graphing:** For the first equation: $$y - 2x = 5 \Rightarrow y = 2x + 5$$ For the second equation: $$2y + x = 0 \Rightarrow 2y = -x \Rightarrow y = -\frac{1}{2}x$$ 3. **Interpretation:** - The first line has slope 2 and y-intercept 5. - The second line has slope $-\frac{1}{2}$ and y-intercept 0. 4. **Graph plotting features:** - The first line crosses the y-axis at (0,5) and rises 2 units for every 1 unit run. - The second line passes through the origin and falls 1 unit vertically for every 2 units traveled horizontally. 5. **Finding the point of intersection (solution to the system):** From $y = 2x + 5$ and $y = -\frac{1}{2}x$, set equal: $$2x + 5 = -\frac{1}{2}x$$ Multiply both sides by 2 to clear the fraction: $$4x + 10 = -x$$ Add $x$ to both sides: $$5x + 10 = 0$$ Subtract 10 from both sides: $$5x = -10$$ Divide both sides by 5: $$x = -2$$ Substitute back to find $y$: $$y = 2(-2) + 5 = -4 + 5 = 1$$ 6. **Conclusion:** The lines intersect at $(-2, 1)$.