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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?
Wiki User
∙ 7y ago
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)
Wiki User
∙ 7y ago
Wiki User
∙ 7y ago2x + y = 1therefore y = 1 - 2x.
Also, x^2 + xy + y^2 = 7
Substitute for y
x^2 + x*(1-2x) + (1-2x)^2 = 7
x^2 + x - 2x^2 + 1 - 4x + 4x^2 = 7
Rearrange: 3x^2 - 3x - 6 = 0
Divide by 3: x^2 - x - 2 = 0
Factorise (x + 1)*(x - 2) = 0
=> x = -1 or x = 2
x = -1 => y = 1 - 2*(-1) = 3
x = 2 => y = 1 - 2*2 = -3
The solutions are (-1, 3) and (2, -3)
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