How would you work out Xsquared+ysquared =25 X-y=1

x² + y² = 25         ...(1)

x - y = 1              ...(2)

Rearrange (2) as x = 1 + y   ...(3)

Put this into (1)

(1 + y)² + y² = 25  so  1 + 2y + y² + y²  = 25  or  2y² + 2y + 1 = 25 or 2y² + 2y - 24 = 0

divide through by 2

y² + y - 12 = 0

This factors as  (y - 3)(y + 4) = 0  so y = 3 or y = -4

Take these two values for y and plug them into (3) to get the corresponding values of x.

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