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: Express y in terms of x from the first equation. Given the first equation: 2x - y = 3 Rearrange to solve for y: -y = 3 - 2x y = 2x - 3 Step 2: Substitute the expression for y into the second equation. Given the second equation: x^2 - xy = -4 Substitute y = 2x - 3: x^2 - x(2x - 3) = -4 Step 3: Solve the resulting quadratic equation for x. Expand the equation: x^2 - 2x^2 + 3x = -4 Combine like terms: -x^2 + 3x = -4 Move all terms to one side to form a standard quadratic equation ax^2 + bx + c = 0: x^2 - 3x - 4 = 0 Factor the quadratic equation: (x - 4)(x + 1) = 0 This gives two possible values for x: x - 4 = 0 x = 4 x + 1 = 0 x = -1 Step 4: Substitute the values of x back into the expression for y to find the corresponding y values. For x = 4: y = 2(4) - 3 y = 8 - 3 y = 5 One solution is (x, y) = (4, 5). For x = -1: y = 2(-1) - 3 y = -2 - 3 y = -5 The second solution is (x, y) = (-1, -5). The solutions to the simultaneous equations are: x = 4, y = 5 and x = -1, y = -5 Send me the next one 📸