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
You are asking to continue the solution for Q2 A) from the image. Your work so far is correct. Q2 A) Find the values of x and y for the equation: (4+i)x + (5-3i)y = 13+i Step 1: Expand the left side of the equation. 4x + ix + 5y - 3yi = 13+i Step 2: Group the real and imaginary parts on the left side. (4x + 5y) + (x - 3y)i = 13+i Step 3: Equate the real parts and the imaginary parts from both sides of the equation. This gives a system of two linear equations: 1. Real parts: 4x + 5y = 13 2. Imaginary parts: x - 3y = 1 Step 4: Solve the system of linear equations. From equation (2), we can express x in terms of y: x = 1 + 3y (*) Step 5: Substitute this expression for x into equation (1). 4(1 + 3y) + 5y = 13 4 + 12y + 5y = 13 4 + 17y = 13 17y = 13 - 4 17y = 9 y = (9)/(17) Your calculation for y is correct. Step 6: Substitute the value of y back into the expression for x from Step 4. x = 1 + 3((9)/(17)) x = 1 + (27)/(17) To add these, find a common denominator: x = (17)/(17) + (27)/(17) x = (17 + 27)/(17) x = (44)/(17) The values are x = (44)/(17) and y = (9)/(17).