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If: 2x+y = 1 then y = 1-2x

If: x^2+xy+y^2 = 7 then x^2+x(1-2x)+(1-2x)^2-7 = 0

So: x^2+x-2x^2+1-4x+4x^2-7 = 0

Collecting like terms: 3x^2-3x-6 = 0 => x^2-x-2 = 0

Solving the above quadratic equation: x = -1 or x = 3

Solutions by substitution: when x = -1 then y = 3 and when x = 2 then y = -3

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Q: What are the solutions to x squared plus xy plus y squared equals 7 and 2x plus y equals 1 with work shown?
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