What are the solutions to the simultaneous equations of x squared plus xy plus y squared equals 7 and 2x plus y equals 1 showing work?

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

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

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

Divide all terms by 3: x^2 -x -2 = 0

Factorizing (x+1)(x-2) = 0 => x = -1 or x = 2

Solutions by substitution: (-1, 3) and (2, -3)