Find the value of X and Y if X^2 + Y^2 = 13 and 2X + Y = 1

Firstly, since only one equation is linear, substitution must be used. This will allow us to make a quadratic equation with one variable and solve for X and Y. To do this, I will make Y the subject of the formula, thus 2X + Y = 1 becomes Y = 1 - 2X. Now, we can substitute this in for Y into the quadratic equation containing two variables, allowing us to form a quadratic equation with a single variable. Therefore, X+ Y= 13 becomes X2 + (1 - 2X)= 13. Now, we can expand the bracket and simplify, forming the quadratic equation: 5X- 4X + 1 = 13. If we equate this equation to 0 and factorise to form (5X + 6)(X - 2) = 0, we can solve to find two solutions for X. Therefore, X must be -6/5 or X must be 2. We can substitute these values of X back into our equation 2X + Y = 1 and solve to find Y. Therefore, Y must be 17/5 or Y must be -3. 

AS
Answered by Alexis S. Maths tutor

6074 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Adam is going to get a loan of £ 720 to help pay for the holiday. Adam will have to pay back the £ 720 plus interest of 15 %. He will pay this back in 12 equal monthly installments. How much money will Adam pay back each month?


The population of sheep on an island is 170. The population of the sheep is expected to increase by 3% each year, what will the population of sheep be in 5 years time? [3 marks]


Solve the equation x^2 + 10x + 24 = 0


Make x the subject of the following formula: 2x-4=2y.


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning