6.1 - Solving Linear Systems Of Equations

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Name:Block:6.1 - Solving Linear Systems of EquationsA system of equations is two or more equations, considered together, involving the same variables.The is all the values of the variables that satisfy each. To solve means:.1. Linear‐linear system – A system of equations involving two linear equations involving thevariables. A graph of this system involves two .The solution to a system of equations from a graph is the point(s) - or ordered pair(s)two graphs . Also called the points.How many solutions are possible?Linear‐linear systemTo solve a system of equations graphically:1.2.3.Example 1: Solve the following system of equations graphically.2𝑥4𝑥4𝑦 16𝑦 5( x, y ) - where the

You try: Solve the following system of equations graphically.𝑥𝑥2𝑦 2 0𝑦 1 06.1 – Solving Linear Systems of Equations (Part 2)You can also use algebraic methods to solve systems of equations. You learned substitution and eliminationmethods in grade 10.Example 1: Solve the following system of equationsa)you try 𝑥 4𝑦 62𝑥 3𝑦 1HW: Solving Linear Systems WS#1

6.1 – Solving Linear Systems of Equations (Part 3)Often it is useful to multiply one or both of the equations in a system to create a specific coefficientin front of one of the variables or to get rid of fractions.Multiply to create -6 coefficient on the x variable:2𝑥3𝑦5Multiply to get rid of all fractions:2𝑥33𝑦41Steps to solve byELIMINATIONExample 1: Solve the following system of equationsa)you try 5𝑥 3𝑦𝑦 25652𝑥HW: Solving Linear Systems WS#2

6.2 – Solving Linear-Quadratic Systems of Equations2. Linear‐quadratic system– A system of equations involving both a linear and quadratic equation involvingthe . A graph of this system involves both aand a .The solution to a system of equations from a graph is the point(s) - or ordered pair(s)two graphs . Also called the points.How many solutions are possible?Linear‐quadratic systemTo solve a system of equations graphically:1.2.3.Solve the following system graphically.a) 3𝑥 𝑦0 𝑥92𝑥 𝑦3( x, y ) - where the

You try a)2𝑥 𝑦𝑥 𝑦 𝑥45𝑥36.2 – Solving Linear-Quadratic Systems of Equations (Part 2)Recall: methods of SOLVING a quadratic equation:1. Graphing𝑞 , if necessary (use p and q formulas)i.Get equation into vertex form: 𝑦 𝑎 𝑥 𝑝ii.Plot the vertex (p, q) follow the directions of the stretch factor ‘a’iii.Determine the coordinates where the parabolas meet2. Factoringi.Combine both equations into one using substitution or eliminationii.Use decomposition (Rainbow Split) method to determine the factors of the quadraticiii.Set each factor equal to zeroiv.Solve for (isolate) the variable3. Quadratic Formulai.Combine both equations into one using substitution or eliminationii.Determine the values of a, b and ciii.Substitute into the formula: 𝑥 to determine the solution(s)HW: Review Solving Quadratics WS

You can also use algebraic methods to solve systems of equations.Recall: steps to solving by SUBSTITUTIONSolve the following system of equations using substitution:a)5 x y 10You try b)x2 x 2 y 04x y 3 02 x2 8x y 3 0HW: System of Equations WS#3

6.2 – Solving Linear-Quadratic Systems of Equations (Part 3)You can also use algebraic methods to solve systems of equations.Recall: steps to solving by ELIMINATIONSolve the following system of equationsa) 𝑦𝑦2𝑥𝑥36𝑥3You try b) 𝑦𝑦16𝑥𝑥12𝑥 5560HW: System of Equations WS#4

6.3 – Solving Quadratic-Quadratic Systems of Equations2. Quadratic‐quadratic system– A system of equations involving two quadratic equations involvingthe same variables. A graph of this system involves two .The solution to a system of equations from a graph is the point(s) - or ordered pair(s)two graphs . Also called the points.How many solutions are possible?Quadratic‐quadratic systemSolve the following system graphically.a) 𝑦𝑦𝑥2𝑥2𝑥6You try b) 𝑦𝑦 𝑥2 𝑥8𝑥485( x, y ) - where the

6.3 – Solving Quadratic-Quadratic Systems of Equations (Part 2 and 3)You can also use algebraic methods to combine the equations. Then use FACTORING or QUADRATIC FORMULA to solve.Solve the following system of equations using substitution:a)3x 2 6 x 2 2 y 0y x2 x 5You try y 2( x 4) 2 5y 2 x 2 16 x 37 0HW: System of Equations WS#5 questions #1-3

Solve the following system of equations using elimination:b)2 x 2 12 x y 18 0 x2 6 x y 3You try x 3x y 2 02x2 y 4 x 3HW: System of Equations WS#5 (finish)

Unit 6 Review1. Solve graphically and verify your solution.y x2 2x 2117y x2 x 4242. Solve by Substitution and verify your solution.3x y 94 x 2 x y 93. Solve by Elimination and verify your solution.x 2 y 46x 2 3 y 93

4. Solve by the method of your choice and verify your solution.a)b)h 4.9t 2 700h 5t 6503x2 4 x y 8 0y 3 2x2 4x

6.3 – Solving Quadratic-Quadratic Systems of Equations 2. Quadratic‐quadratic system– A system of equations involving two quadratic equations involving the same variables. A graph of this system involves two _. The solution to a system of equations from a graph is the point(s) - or ordered pair(s) (,)x y - where the

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