1. **State the problem:** We need to complete the tables of values for the lines $y=\frac{1}{4}x+5$ and $y=-2x+\frac{1}{2}$, plot them, and then solve the simultaneous equations graphically. 2. **Complete the tables:** For $y=\frac{1}{4}x+5$: - When $x=-4$, $y=\frac{1}{4}(-4)+5 = -1 + 5 = 4$ - When $x=0$, $y=\frac{1}{4}(0)+5 = 0 + 5 = 5$ - When $x=4$, $y=\frac{1}{4}(4)+5 = 1 + 5 = 6$ For $y=-2x+\frac{1}{2}$: - When $x=-1$, $y=-2(-1)+\frac{1}{2} = 2 + 0.5 = 2.5$ - When $x=0$, $y=-2(0)+\frac{1}{2} = 0 + 0.5 = 0.5$ - When $x=1$, $y=-2(1)+\frac{1}{2} = -2 + 0.5 = -1.5$ 3. **Plot the points:** - For $y=\frac{1}{4}x+5$: points $(-4,4)$, $(0,5)$, $(4,6)$ - For $y=-2x+\frac{1}{2}$: points $(-1,2.5)$, $(0,0.5)$, $(1,-1.5)$ 4. **Solve the simultaneous equations graphically:** The solution is the point where the two lines intersect. 5. **Find the intersection algebraically:** Set $\frac{1}{4}x + 5 = -2x + \frac{1}{2}$ Multiply both sides by 4 to clear fractions: $$x + 20 = -8x + 2$$ Bring all terms to one side: $$x + 8x = 2 - 20$$ $$9x = -18$$ Divide both sides by 9: $$x = -2$$ Substitute $x=-2$ into $y=\frac{1}{4}x + 5$: $$y = \frac{1}{4}(-2) + 5 = -\frac{1}{2} + 5 = 4.5$$ 6. **Final answer:** The lines intersect at $\boxed{(-2, 4.5)}$. This is the solution to the simultaneous equations.