SOLUTION: Solve the system x^2 + y = 3 x + y = 1

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Question 743011: Solve the system
x^2 + y = 3
x + y = 1
Answer by davethejackal(28) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
+x%5E2+%2B+y+=+3+ [1]
+x+%2B+y+=+1+ [2]
Subtracting x^2 from both sides of [1] gives +y=+3+-+x%5E2+ [3]
Subtracting x from both sides of [2] gives +y+=+1-x+ [4]
Combining [3] and [4] +y+=+3+-+x%5E2+=+1-x+
Thus +x%5E2+-x+-2+=+0+

Factorising gives +%28x-2%29%28x%2B1%29+=+0+

Hence x=2 or x = -1

Subst x=2 in [3] gives +y+=+3-+2%5E2+=-1+
Subst x=-1 in [3] gives
Subst x=-1 in [4] gives +y+=+1-x+=+2+

Hence the solutions are (2,-1) and (-1,2)