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
Step 1: Cross-multiply the given equation to eliminate the denominators. jx(x+3y) = (3x+j4)(1+jy) Step 2: Expand both sides of the equation. The left side becomes: jx^2 + j3xy The right side becomes: 3x(1) + 3x(jy) + j4(1) + j4(jy) 3x + j3xy + j4 + j^24y Since j^2 = -1, substitute this into the equation: 3x + j3xy + j4 - 4y Group the real and imaginary terms on the right side: (3x - 4y) + j(3xy + 4) Step 3: Equate the real and imaginary parts of the expanded equation. The full equation is: jx^2 + j3xy = (3x - 4y) + j(3xy + 4) We can write the left side as 0 + j(x^2 + 3xy). Equating the real parts: 0 = 3x - 4y (*) Equating the imaginary parts: x^2 + 3xy = 3xy + 4 (**) Step 4: Solve the system of equations. From equation (**), we can cancel 3xy from both sides: x^2 = 4 x = ± sqrt(4) x = ± 2 Now, use equation (*) to find the corresponding values of y: 3x - 4y = 0 4y = 3x y = (3)/(4)x For x = 2: y = (3)/(4)(2) = (6)/(4) = (3)/(2) For x = -2: y = (3)/(4)(-2) = -(6)/(4) = -(3)/(2) The solutions for x and y are: x=2, y=(3)/(2) and x=-2, y=-(3)/(2) That's 2 down. 3 left today — send the next one.