advertisement

ALGEBRA 2 LECTURE S – 1: Solving Systems by Graphing or Substitution Reading Assignment: Chapter 3, Pages 156 – 161 SYSTEMS OF EQUATIONS A SYSTEM OF EQUATIONS is a collection of equations in the same variables. The solution of a system of two linear equations in x and y is any ordered pair (x. y) that satisfies both equations. The solution (x, y) is also the point of intersection for the graphs of the lines in the system. CLASSIFYING SYSTEMS OF EQUATIONS If a system of equations has at least one solution, it is called CONSISTENT. o If a system has exactly one solution it is called INDEPENDENT. o If a system has infinitely many solutions, it is call DEPENDENT. If a system does not have a solution, it is called INCONSISTENT. Classifying using Algebra If solving using the addition or substitution method leads to: x = a number, y = a number then the system is: and the equations: INDEPENDENT will have different values of m when both are placed in y = mx + b (slope-intercept) form will have the same value of m, but different values of b, when both are placed in y = mx + b form will be identical when both are placed in slope-intercept form an inconsistent equation, such as 0 = 3 INCONSISTENT An identity, such as 5 = 5 DEPENDENT Classifying by Graphing If the equations have: Different Slopes Same Slope but Different Intercepts Same Slope and Same Intercept INDEPENDENT y = x + 10 y = 2x then the system is: INDEPENDENT INCONSISTENT and the lines: cross at a point are parallel and never cross DEPENDENT are actually both the same line INCONSISTENT y=x y = x + 10 DEPENDENT y = x + 10 2y = 2x + 20 ALGEBRA 2 LECTURE S – 1: Solving Systems by Graphing or Substitution EXAMPLE 1: Graph and classify each system. Then find the solution from the graph. A. x + y = 5 and x – 5y = –7 B. x – 2y = 3 and x + 5 = 2y TRY THIS Page 157: Graph and classify: y = 3x + 4 and y = –2x + 4. Then find the solution from the graph. EXAMPLE 2: Use substitution to solve the system: 2x + y = 3 and 3x – 2y = 8. Check your solution. TRY THIS Page 158: Use substitution to solve the system: 3x + y = 8 and 18x + 2y = 4. Check your solution. HW S – 1 Page 161 #17 – 31 ODDS