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
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