Solve: -x+y=4 and y=(x^2)-4x+2

Identify each system as linear-quadratic or quadratic-quadratic. Then solve the systems.
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1 Answer

-x+y=4, y=x+4=x2-4x+2,

x2-5x=2, complete the square:

x2-5x+25/4=2+25/4,

(x-5/2)2=33/4,

(x-5/2)2-(√33/2)2=(x-5/2+√33/2)(x-5/2-√33/2).

Therefore x=5/2-√33/2 or 5/2+√33/2.

Approx solution: x=-0.3723 or 5.3723; y=x+4=3.6277 or 9.3723 respectively.

by Top Rated User (1.2m points)

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