Solve the following simultaneous equations algebraically [6] y= x-3, y=2x^2 + 8x -7
This question is asking you to solve, therefore you need to show detailed working out in logical steps to show the examiner how you reach your solution. To solve simultaneous equations we first need to eliminate one of the variables, either x or y In this question it makes most sense to eliminate y since both equations are written in a 'y=' format We can set both equations equal to each other to obtain: x-3 = 2x2 + 8x -7From here we can collect like terms by rearranging around the = sign 2x2 + 7x - 4 = 0Ideally we want to write our equation so that it is equal to zero, this is because we are looking for a solution, in a quadratic equation a solution is when the line crosses the x axis, or in other words, when the x coordinate is zero.Since the question acts for an algebraic solution, we need to factorise using 2 brackets to obtain...(2x – 1)(x + 4) = 0Set each bracket to zero individually to obtain x values of 1/2 and -4Substitute these x values into the equation y= x-3, to obtain y values of - 2 1/2 and -7Remember to obtain both x and y values for full marks
