This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems: 1. Solve the following simultaneous equation using the elimination method: The given equations are: 2x + 3y = 12 (i) 3x - y = 7 (ii) Step 1: Multiply equation (ii) by 3 to make the coefficients of y opposites. 3 × (3x - y) = 3 × 7 9x - 3y = 21 (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 = (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 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 0.004560. 3 done, 2 left today. You're making progress.