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

y = x - 2

y+ x2 = 10

  1. Subsitutute the top equation into the second equation:

     (x-2)2 + x2 = 10

  1. Expand out the brackets and simplify:

     x- 4x + 4 + x= 10

     2x- 4x - 6 = 0

     x2 - 2x - 3 = 0

  1. Factorise the quadratic equation to find the two values of x:

    (x - 3) (x + 1) = 0

    x = 3, x = -1

         

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Answered by Iman R. Maths tutor

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