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
Right ~Excel, let's go. Step 1: Express one variable in terms of the other from the linear equation. The given equations are: 1) 2x - y = 0 2) 4x^2 + 3y^2 - 2x + y = 16 From equation (1), we can express y in terms of x: y = 2x Step 2: Substitute this expression for y into the second equation. Substitute y = 2x into equation (2): 4x^2 + 3(2x)^2 - 2x + (2x) = 16 Step 3: Simplify and solve the resulting quadratic equation for x. 4x^2 + 3(4x^2) - 2x + 2x = 16 4x^2 + 12x^2 = 16 16x^2 = 16 Divide both sides by 16: x^2 = (16)/(16) x^2 = 1 Take the square root of both sides: x = ±sqrt(1) x = ± 1 So, we have two possible values for x: x_1 = 1 and x_2 = -1. Step 4: Find the corresponding values for y using y = 2x. For x_1 = 1: y_1 = 2(1) y_1 = 2 This gives the solution pair (1, 2). For x_2 = -1: y_2 = 2(-1) y_2 = -2 This gives the solution pair (-1, -2). The solutions to the pair of equations are (x, y) = (1, 2) and (x, y) = (-1, -2). Send me the next one 📸