Systems of Equations. OBJECTIVES To understand what a system of equations is. Be able to solve a system of equations from graphing, substitution, or elimination.

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Presentation transcript:

Systems of Equations

OBJECTIVES To understand what a system of equations is. Be able to solve a system of equations from graphing, substitution, or elimination Determine whether the system has one solution, no solution, or an infinite amount of solutions.

Defining a System of Equations A grouping of 2 or more equations, containing one or more variables. x + y = 2 2x + y = 5 2y = x + 2 y = 5x - 7 6x - y = 5

Solution? Is (-3, 4) a solution to the system?

Types of Solutions Intersecting Lines have ONE unique solution. Coincidental Lines (or same lines) have MANY solutions. Parallel Lines have NO solutions!

Solving Systems by Graphing

Graphing Calculator

Examples… 1) Determine whether the following have one, none, or infinite solutions by looking at the slope and y-intercepts 2y + x = 8 y = 2x + 4 3)2) x - 5y = 10 -5y = -x +6 y = -6x + 8 y + 6x = 8 ANS: One Solution ANS: No Solution ANS: Infinite Solutions

Solutions Solve by graphing

Solving Systems by Substitution

Example Solve the system by substitution.

Try One! Solve the system by substitution.

Solving Systems by Elimination

Elimination We can solve by elimination by either Adding or Subtracting two equations to eliminate a variable!

Example Solve by Elimination

Example Solve by Elimination

Try Some! Solve the systems by elimination. 1.2.

More with Elimination If one will not cancel, multiply one or both equations to get variables to cancel

Example Solve the system by elimination.

Special Solutions Solve each system by elimination. 1.2.