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
Okay, let's tackle these questions. a) Solve the simultaneous equations: 3x + 2y = 11 (1) 2x - y = 1 (2) Step 1: Multiply equation (2) by 2 to eliminate y. 2(2x - y) = 2(1) 4x - 2y = 2 (3) Step 2: Add equation (1) and equation (3). (3x + 2y) + (4x - 2y) = 11 + 2 7x = 13 x = (13)/(7) Step 3: Substitute the value of x into equation (2) to find y. 2((13)/(7)) - y = 1 (26)/(7) - y = 1 y = (26)/(7) - 1 y = (26)/(7) - (7)/(7) y = (19)/(7) The solution is: x = (13)/(7), y = (19)/(7) b) If 5^x = 243, find x. Step 1: Take the logarithm of both sides of the equation. (5^x) = (243) Step 2: Use the logarithm property (a^b) = b (a) to bring x down. x (5) = (243) Step 3: Solve for x. x = ((243))/((5)) Step 4: Calculate the value using a calculator and round to two decimal places as per the instructions. x ≈ (2.385606)/(0.698970) x ≈ 3.4130 x ≈ 3.41 The value of x is: x ≈ 3.41 Last free one today — make it count tomorrow, or type /upgrade for unlimited.