SOLUTION: given the equations: y= x^2-6x+10 y+x=4 what is the solution to the given system of equations

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Question 604144: given the equations: y= x^2-6x+10 y+x=4 what is the solution to the given system of equations
Answer by alicealc(281) About Me  (Show Source):
You can put this solution on YOUR website!
y=+x%5E2-6x%2B10

y%2Bx=4
y+=+4+-+x
substitute this into first equation:
y=+x%5E2-6x%2B10
4+-+x=+x%5E2-6x%2B10
0=+x%5E2-6x%2B10-4%2Bx
0=+x%5E2-5x%2B6
0=%28x+-+3%29%2A%28x+-+2%29
x - 3 = 0 or x - 2= 0
x = 3 or x = 2

if x = 3 then y = 4 - x = 4 - 3 = 1
if x = 2 then y = 4 - y = 4 - 2 = 2

so, the solutions are:
{(3,1), (2,2)}