Solve the following simultaneous equation: y= x^2 - 3x + 4 y - x = 1

When it comes to solving simultaneous equations the way you structure your working out will really help you get to the correct answer. The layout can be used for all simultaneous equations and will make even the more complicated ones seem a lot less daunting. Firstly label the two equations: y= x² - 3x + 4  (1) and y - x = 1 (2). Substitute (1) into (2). x² - 3x + 4 - x = 1 This equation becomes (3). Solve (3) by putting all the terms onto one side making sure x² stays positive to simplify. x² - 4x + 3 = 0. Now factorise the equation(x-3)(x-1) = 0. Either x - 3 = 0 or x-1=0, therefore x = 3 or x = 1. Now substitute each possible answer into the simplest simultaneous equation which would be (2) to solve for y. When x = 3 y - 3 = 1 y = 4 When x = 1 y - 1 = 1 y = 2.