Solve algebraically the simultaneous equations x^2 + y^2 = 25 and y - x = 1

Let's label the equations x2 + y2 = 25 (1) y - x = 1 (2). We can use substitution to solve this simultaneous equation. Let's make y the subject of the equation (2) and we get y = x + 1. Now, lets find y2 and get y2 = (x + 1)2 = (x + 1)(x + 1) = x2 + 2x + 1. Now we can substitute y2 into equation (1) and get the following:x2 + x2 + 2x + 1 = 25 => 2x2 + 2x -24 = 0 => x2 + x - 12 = 0. Factorising gives us (x + 4)(x - 3) = 0 and the roots are x = -4 and x = 3Now we need to find y by substituting x into y = x + 1 and we get y = -3 and y = 4. Therefore, the solutions are x = -4, y = -3 and x = 3, y = 4.

Answered by Vithya N. Maths tutor

8152 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Simplify (a) p^2× p^5 (b) Simplify g^6 ÷ g^4


Express 60 as a product of its prime factors.


There are n sweets in a bag, 6 are orange, the rest yellow. Two sweets are taken out individually without replacement. The probability of which is 1/3. show n²-n-90=0


Solve the following simultaneous equation: 3x+y= 11 and 2x+y=8.


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