Solving Quadratic Systems - ClassZone

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Page 1 of 2632Chapter 10Quadratic Relations and Conic SectionsSolving Quadratic SystemsSOLVING ASYSTEM OFEQUATIONSIn Lesson you studied two algebraic techniques for Solving a system of linear equations . You can use the same techniques (substitution and linearcombination) to solve Quadratic Points of IntersectionFind the points of intersection of the graphs of x2+ y2= 13 and y = x+ find the points of intersection, substitute x+ 1for yin the equation of the + y2= 13Equation of circlex2+ (x+ 1)2= 13Substitute x+1 for + x2+ 2x + 1 = 13Expand the + 2x 12 = 0Combine like (x 2)(x+ 3) = 2 or x= 3Zero product propertyYou now know the x-coordinates of the points of intersection. To find the y-coordinates, substitute x= 2 and x = 3 into the linear equation and solve for y.

Solving Quadratic Systems SOLVING A SYSTEM OF EQUATIONS In Lesson 3.2 you studied two algebraic techniques for solving a system of linear equations. You can use the same techniques (substitution and linear combination) to solve quadratic systems. Finding Points of Intersection

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