Solve the simultaneous equations: x^2 + 8x + y^2; x - y = 10.

Label the two equations.

x2 + 8x + y2 = 84 (1)
x - y = 10 (2)

Rearrange (2) to get y = x - 10 and substitute for y in (1) to get x2 + 8x + (x - 10)2 = 84. Expanding and collecting like terms gives 2x2 -12x + 16 = 0 (3). Dividing (3) through by 2 gives x2 - 6x + 8 = 0 (4). Factorising (4) gives (x - 2)(x - 4) = 0 so either x = 2 and y = -8 or x = 4 and y = -6.

LT
Answered by Lewis T. Maths tutor

4848 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Prove that 2 cot (2x) + tan(x) == cot (x)


Find the derivative of the curve e^(xy) = sin(y)


Given y = 2x(x^2 – 1)^5, show that dy/dx = g(x)(x^2 – 1)^4 where g(x) is a function to be determined.


A circle with centre C(2, 3) passes through the point A(-4,-5). (a) Find the equation of the circle in the form (x-a)^2 + (y-b)^2=k


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences