# Maths (Linear and Quadratic Equations)

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I need to solve a pair of equations where one is linear and the other is quadratic.

2x2 + 3xy + y2 = 0
3x + y = 2

last 2 in 2x2 is square root two, same after y2.

• Maths (Linear and Quadratic Equations) -

just substitute the linear into the quadratic:

y = 2-3x
2x^2 + 3x(2-3x) + (2-3x)^2 = 0
2x^2 + 6x - 9x^2 + 4 - 12x + 9x^2 = 0
2x^2 - 6x + 4 = 0
2(x-1)(x-2) = 0
solutions: (1,-1)(2,-4)

or,
2x^2 + 3xy + y^2 = 0
(2x+y)(x+y) = 0
y = -2x or y = -x

3x+(-2x) = 2
x = 2, so y = -4

3x+(-x) = 2
x = 1, so y = -1

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