 # Solving System of Equations Using Graphing

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Solving System of Equations Using Graphing
What does a graph of an equation show us?  ALL the solutions to the equation How many solutions are there?  Infinite number In order for there to be a unique solution to an equation,  there must be a second condition placed on the solution  set, i.e. the solution must satisfy two equations  simultaneously.

Solving Linear Systems of Equations
Methods for Solving: 1). Graphing 2). Substitution Method 3). Linear Combinations linear system: two or more linear equations in the same variables solution of a linear system: point that makes both equations true

A: Checking Solutions ex 1: -2x + y = 2 x + y = -1 for (-1, 0)
Check to see if the given point is a solution to both equations ex 1: x + y = x + y = -1 for (-1, 0) ex 2: x + 3y = x + y = 6 for (3, -6)

B: Finding solutions using graphing
Graph each line to find the value of x and y that satisfy  both equations.  x + y = 3 and 2x  y = 0

Graph the equations to solve the linear system
2.) y = 2x  4 y = x + 1 2

Since the solution is the point of intersection, there are three possibilities for graphs of the lines 1.) intersect at one point 2.) same line 3.) no intersection (parallel) no solution

intersecting lines parallel lines solution: (3, 3) solution: no solution lines coincide solution: infinite solutions

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