Algebra 1 Mini Posters Systems of Linear and Quadratic Equations May 24, 2017 Systems of Linear and Quadratic Equations Snapshot What are solutions? Mini Posters

Systems of Linear Equations and Quadratics

Systems of Linear Equations and Quadratics

Systems of Linear Equations and Quadratics

Systems of Linear Equations and Quadratics Solutions!! Solutions to systems of linear and quadratic equations are points of intersection

Systems of Linear Equations and Quadratics Solutions: Three possible cases

Systems of Linear Equations and Quadratics Solutions: How are systems solved? (How can the points of intersection be found?) 𝑦= 𝑥 2 −5𝑥+7 𝑦=2𝑥+1 Set equations equal to each other 2𝑥+1= 𝑥 2 −5𝑥+7 2) Now solve the quadratic!

Systems of Linear Equations and Quadratics Solutions: How are systems solved? (How can the points of intersection be found?) 2) Now solve the quadratic! 2𝑥+1= 𝑥 2 −5𝑥+7 −2𝑥 −2𝑥 1= 𝑥 2 −7𝑥+7 −1 −1 0= 𝑥 2 −7𝑥−6

Systems of Linear Equations and Quadratics Solutions: How are systems solved? (How can the points of intersection be found?) 2) Now solve the quadratic! 0= 1𝑥 2 −7𝑥−6 −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 −(−7)± (−7) 2 −4 1 −6 2 1

Systems of Linear Equations and Quadratics Solutions: How are systems solved? (How can the points of intersection be found?) 2) Now solve the quadratic! 𝒙≈𝟕.𝟕𝟕 𝒙≈−𝟎.𝟕𝟕 Finally…. Substitute each x-value back into one of the original equations, and find y! 𝑦= 𝑥 2 −5𝑥+7 𝑦=2𝑥+1

Systems of Linear Equations and Quadratics 𝒙≈𝟕.𝟕𝟕 𝒙≈−𝟎.𝟕𝟕 Finally…. Substitute each x-value back into one of the original equations, and find y! 𝑦= 𝑥 2 −5𝑥+7 𝑦=2𝑥+1 First Solution!!! 𝟕.𝟕𝟕,𝟏𝟔.𝟓𝟒 𝑦=2 7.77 +1 𝑦=2 𝑥 +1

Mini-Posters Requirements: System of Equations written on paper System of Equations solved w/ process Graph of your system, w/ marking of solutions! Optional: Color! Pictures or drawings!