Solve the simultaneous equations: x^2 + y^2 = 10 and x + 2y = 5

1.)x2 + y2 = 10 2.)x + 2y = 5. Rearrange 2nd equation: x = 5 - 2y. Substitute back into 1st equation: (5 - 2y)2 + y2 = 10. Multiply out brackets: 4y2 - 20y + 25 + y2 = 10. Rearrange equation: 5y2 - 20y + 15 = 0. Simplify equation: y2 - 4y + 3 = 0. Factorise: (y-3)(y-1) = 0. Therefore: y = 3 or y = 1. Sub values of y back into equation 2 to find x values. When y = 3: x + 2(3) = 5, so x + 6 =5, therefore x = -1 and so the coordinates are (-1, 3). When y = 1: x + 2(1) = 5, so x + 2 = 5, therefore x = 3 and so coordinates are (3, 1). To check sub x and y values into equations and see if you get the correct answers

Answered by Edward W. Maths tutor

9171 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the integral of ln(x)


A curve has equation x^2 + 2xy – 3y^2 + 16 = 0. Find the coordinates of the points on the curve where dy/dx =0


Line AB, with equation: 3x + 2y - 1 = 0, intersects line CD, with equation 4x - 6y -10 = 0. Find the point, P, where the two lines intersect.


Find the integral between 4 and 1 of x^(3/2)-1 with respect to x


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