Solve the simultaneous equations: y = x + 6, x^2 + 2y = 9

y = x + 3x2 + 2y = 9We want to make the squared equation have either only x's or only y's, so we substitute y = x + 3 into the equation:x2 + 2(x + 3) = 9We need to take out the brackets, and simplify this equation.x2 + 2x + 6 = 9x2 + 2x - 3 = 0This is now in the form of a quadratic, so we can solve it:x2 + 2x - 3 = 0(x + 3)(x - 1) = 0 so therefore, x = -3, x = 1These answers for the x-values can give us the y-values, if we substitute them into the original equation:When x = -3, y = -3 + 3 y = 0When x = 1 y = 1 + 3 y = 4We can check our answers by substituting them into the original equation:x = -3, y = 0] (3)2 + 2(0) = 9 = CORRECTx = 1, y = 4] (1)2 + 2(4) = 1 + 8 = 9 = CORRECT

Answered by Hayley H. Maths tutor

2909 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How would you solve 4x > 7 - 10x ?


Bob sprints down a 100 metre track as fast as he can and as he arrives at the finish, a light gate cuts a timer that has been active since Bob began his sprint. It reads 12.45 seconds. calculate Bobs average speed during the sprint.


Solve the quadratic equation x^2 + x - 6 = 0


Expand and simplify x(x+4)(x-5)


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences