1. Stating the problem: Plot the graph of the system of linear simultaneous equations: $$y-2x=5$$ $$2y+x=0$$ 2. Rearrange each equation in terms of $y$: From the first equation: $$y=2x+5$$ From the second equation: $$2y=-x \implies y=\frac{-x}{2}$$ 3. These two equations represent two lines: Line 1: $$y=2x+5$$ Line 2: $$y=\frac{-x}{2}$$ 4. To find their intersection, solve the system: Set their $y$ values equal: $$2x+5=\frac{-x}{2}$$ Multiply both sides by 2 to clear the fraction: $$4x+10=-x$$ Add $x$ to both sides: $$5x+10=0$$ Subtract 10: $$5x=-10$$ Divide by 5: $$x=-2$$ 5. Substitute $x=-2$ to find $y$: Using first equation: $$y=2(-2)+5=-4+5=1$$ 6. The lines intersect at the point $(-2,1)$. This means the system has a unique solution. 7. For the graph, plot the lines: Line 1 passes through $(0,5)$ and $(1,7)$. Line 2 passes through $(0,0)$ and $(2,-1)$. Plotting these lines will show their intersection at $(-2,1)$.