Solve the given system:

y=x^2+4x-9         (1)

 

x+2y=3               (2)

 

Replace y in (2) using (1):

x + 2x^2 + 8x - 18 = 3

 

Rearrange:

2x^2 + 9x - 21 = 0

 

Solve for x using the quadratic formula to get:

 

x₊ = (-9 + sqrt(249))/4   and x_- =  (-9 - sqrt(249))/4

 

Use these in (2) and rearrange to get the corresponding values of y as:

 

y₊ = (21 - sqrt(249))/8   and y_- = (21 + sqrt(249))/8

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