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

This question is slightly trickier than normal simultaneous equations, because we have values to the power of 2. What we can do is make either y or x the subject of the 2nd equation (y-x = 3). For this example, I will choose to make y the subject, which then gives us y = 3 + x. We can use this equation, and substitute it into the value of "y" in the 1st equation, as follows --> x^2 + (3+x)^2 = 29 We can then expand the brackets and simplify: x^2 + x^2 + 6x + 9 = 29 2x^2 + 6x -20 = 0 (it is important to make the equation equal to 0 so that we can solve the equation to find the values of x) x^2 + 3x - 10 = 0 (we can divide the whole equation by 2, as this is a common factor) (x + 5) (x - 2) = 0 (we can factorise the equation to give us 2 brackets; we have found two numbers which multiply to give -10 and add to give +3) .˙. x = -5 and x = 2 (each bracket is made equal to 0 and solved separately, we have two values for x because this is a quadratic equation)Each value is then substituted back into the rearranged 2nd equation (y = 3 + x) which gives us y = -2 and y = 5

Answered by Trushna D. Maths tutor

2945 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5 Work out the area of the triangle.


The probability that it rains on a given day is 0.15. The probability that a football match is cancelled when it rains is 0.65. If it doesn't rain, the probability that the match is not cancelled is 0.95. What is the chance that the match is cancelled?


How would you solve a simultaneous equation?


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?


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 2013–2024

Terms & Conditions|Privacy Policy
Cookie Preferences