Here are the solutions to the problems: 1. Solve the following simultaneous equation using the elimination method: The given equations are: $$ 2x + 3y = 12 \quad \text{(i)} $$ $$ 3x - y = 7 \quad \text{(ii)} $$ Step 1: Multiply equation (ii) by 3 to make the coefficients of $y$ opposites. $$ 3 \times (3x - y) = 3 \times 7 $$ $$ 9x - 3y = 21 \quad \text{(iii)} $$ Step 2: Add equation (i) and equation (iii) to eliminate $y$. $$ (2x + 3y) + (9x - 3y) = 12 + 21 $$ $$ 11x = 33 $$ Step 3: Solve for $x$. $$ x = \frac{33}{11} $$ $$ x = 3 $$ Step 4: Substitute the value of $x=3$ into equation (ii) to solve for $y$. $$ 3(3) - y = 7 $$ $$ 9 - y = 7 $$ $$ -y = 7 - 9 $$ $$ -y = -2 $$ $$ y = 2 $$ The solution is $\boxed{x=3, y=2}$. 2. Write 0.00456 to 4 significant figures. Step 1: Identify the first non-zero digit. The first non-zero digit in 0.00456 is 4. Step 2: Count four significant figures starting from the first non-zero digit. The significant figures are 4, 5, 6. This is only 3 significant figures. To express the number to 4 significant figures, we add a trailing zero. $$ 0.004560 $$ The number 0.00456 to 4 significant figures is $\boxed{0.004560}$. 3 done, 2 left today. You're making progress.