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

y = x - 2

y²+ x² = 10

Subsitutute the top equation into the second equation:

(x-2)² + x² = 10

Expand out the brackets and simplify:

x²- 4x + 4 + x²= 10

2x²- 4x - 6 = 0

x² - 2x - 3 = 0

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

(x - 3) (x + 1) = 0

x = 3, x = -1

IR

Answered by Iman R. • Maths tutor

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