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Section 3.5: Systems of Linear Equations in Two Variables System of Linear Equations: A set of linear equations in the same 2 variables Solution: Any ordered pair of numbers that is a solution of each equation in the system Equivalent Systems: Systems that have the same solution set Consistent: A system that has at least one solution ...equations that will intersect Inconsistent: A system that has no solution ...equations that are parallel Algebra 2: Section 3.5 1 Section 3.5: Systems of Linear Equations in Two Variables Example: Solve the system. If it has an infinite solution, give 3 solutions. x + y = 9 ; x - y = 13 Method 1: Substitution Method 2: Linear Combination (Stack 'em) Algebra 2: Section 3.5 2 Section 3.5: Systems of Linear Equations in Two Variables Example: Solve the system. If it has an infinite solution, give 3 solutions. 2x - 3y = 7 ; 3x + y = 5 Algebra 2: Section 3.5 3 Section 3.5: Systems of Linear Equations in Two Variables Example: Solve the system. If it has an infinite solution, give 3 solutions. x + y = 3x - 1 ; -2x + y = -1 Algebra 2: Section 3.5 4