Solve the simultaneous equations algebraically: y = x+19 AND y = x^2 + 4x +1.

We have one linear and one quadratic equation here. Since we have a quadratic, we will have two sets of solutions. Let's solve by substitution. Substitute equation (1) into equation (2), which yields:x + 19 = x^2+4x+1OR 0 = x^2 + 3x - 18To solve this quadratic to find our x values we must first factorise, which gives:0 = (x+6)(x-3)It must follow that:x = -6 OR x = 3.Sub these two distinct real solutions into equation 1, we will get our corresponding y value:x = -6, y = 13 OR x=3, y=22.

LD
Answered by Liam D. Maths tutor

3153 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Factorise and solve x^2 + 3x - 4 = 0


GCSE 2011: Solve the simultaneous equations: y^2 = 2x + 29 and y = x - 3


Three points have coordinates A(-8, 6), B(4, 2) and C(-1, 7). The line through C perpendicular to AB intersects AB at the point P. Find the equations of the line AB and CP.


Solve the following simultaneous equations: y - 2x = 6 and y + 2x = 0


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