1. **State the problem:** We need to find the missing values A, B, C, and D in the tables for the simultaneous equations: $$y + 9x = 0$$ $$2y - x = 0$$ 2. **Use the first equation $y + 9x = 0$ to find A and B:** - When $x=0$, substitute into the equation: $$y + 9(0) = 0 \implies y = 0$$ So, $A = 0$. - When $x=1$, substitute: $$y + 9(1) = 0 \implies y + 9 = 0 \implies y = -9$$ So, $B = -9$. - When $x=2$, $y$ is given as $-18$, which matches: $$y + 9(2) = -18 + 18 = 0$$ 3. **Use the second equation $2y - x = 0$ to find C and D:** - When $x=0$, substitute: $$2y - 0 = 0 \implies 2y = 0 \implies y = 0$$ So, $C = 0$. - When $x=1$, substitute: $$2y - 1 = 0 \implies 2y = 1 \implies y = \frac{1}{2}$$ So, $D = \frac{1}{2}$. - When $x=2$, $y$ is given as $1$, check: $$2(1) - 2 = 2 - 2 = 0$$ 4. **Final answers:** $$A = 0, B = -9, C = 0, D = \frac{1}{2}$$