How do I solve simultaneous equations when one is quadratic? For example 3x^2 -2y = 19, 6x-y-14=0

The aim of this question is to find the two solutions which satisfy the quadratic equation. The approach to this can be broken down into a few principle steps: 1) Express y in terms of x. Here 6x-y-14=0 can be simply rearranged to y = 6x-14 2) Substitute this new definition of y into the other equation so that we have a quadratic equation, all in terms of x3x^2 -2y = 19 becomes 3x^2 -2(6x-14) = 19, which can be rearranged to the quadratic x^2-4x+3 = 03) Solve the quadratic for x: Rearrange the formula to (x-1)(x-3) = 0, which gives the two solutions for x as 3 or 1 4) To complete the solution by solving the value of y for each of the two x values:Considering y=6x-14, When x=1, y = 6x1-14 = -8; By the same substitution, when x =3, y = 4

Answered by Angus M. Maths tutor

2181 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do you simplify expressions involving different powers?


Factorise the following- A) 4x+12xz. B) 3xy + 6y d) 4A^2B^2+ 8AB^2 +16AB^3


What is the difference between the mode, median and mean?


Simplify fully 3(3 – x) – 2(x – 4)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences