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.

AP
Answered by Anisha P. Maths tutor

6046 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

What is Pythagoras's theorem?


Sketch a graph of the equation of y=3x+2


How do I know which rule of trigonometry to apply in a question?


Given 6x+2y=4 and 5x+y=8, solve the simultaneous equations to find x and y.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning