Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables.

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Presentation transcript:

Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables

Systems of Linear Equations and Their Solutions Two linear equations in two variables are called a system of linear equations. A solution to a system of linear equations is the set of ordered pairs which satisfy both equations. A system of linear equations may have –no solutions –1 solution –Infinite solutions What does this mean graphically?

Examples Checking a solution to a system of equations Exercise Set 7.3 #3 Determine if (2,5) is a solution to the system 2x + 3y = 17 x + 4y = 16

Examples Solving a system by graphing Exercise Set 7.3 #9 Solve by graphing, check the solution y = x + 5 y = -x + 3

Examples Solving a system by substitution Exercise Set 7.3 #15 Solve by substitution, check the solution x + 3y = 8 y = 2x - 9 Solving a system by addition method. Exercise Set 7.3 #27 Solve by the addition method, check the solution 2x + 3y = 6 2x – 3y = 6

More Examples Exercise Set 7.3 #23, 37 Solve by both methods x + 8y = 6 2x + 4y = -3 Solve by either method x = 9 - 2y x + 2y = 13

Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations