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: Write down the given system of equations. We are given two equations: 1) xy = 4 2) x+y = 5 Step 2: Express one variable in terms of the other from one of the equations. From equation (2), we can express y in terms of x: y = 5 - x Step 3: Substitute this expression into the other equation. Substitute y = 5 - x into equation (1): x(5 - x) = 4 Step 4: Simplify and solve the resulting quadratic equation. Distribute x: 5x - x^2 = 4 Rearrange the terms to form a standard quadratic equation (ax^2 + bx + c = 0): x^2 - 5x + 4 = 0 Factor the quadratic equation. We need two numbers that multiply to 4 and add to -5. These numbers are -1 and -4. (x - 1)(x - 4) = 0 This gives two possible values for x: x - 1 = 0 x = 1 x - 4 = 0 x = 4 Step 5: Find the corresponding values for y using y = 5 - x. Case 1: If x = 1 y = 5 - 1 = 4 Case 2: If x = 4 y = 5 - 4 = 1 The solutions for the system of equations are: (x,y) = (1,4) or (4,1) Last free one today — make it count tomorrow, or type /upgrade for unlimited.