Systems of Equations Solving by Graphing

System of Equations When solving a system of equations, you are looking for the point that would satisfy both equations (make them true)…think of it as the point of intersection or when both equations contain the same (x,y) coordinate.

Systems of Equations One way to solve equations that involve two different variables is by graphing the lines of both equations on a coordinate plane. If the two lines cross the solution for both variables is the coordinate of the point where they intersect.

y = 2x + 0 & y = -1x + 3 Up 2 and right 1 Up 1 and left 1 (1,2) Slope = 1/-1 Y Slope = 2/1 y-intercept= 0 X Up 2 and right 1 Up 1 and left 1 y-intercept= +3 (1,2) The solution is the point they cross at (1,2)

y = x - 3 & y = -3x + 1 Slope = 3/-1 Slope = 1/1 y-intercept= -3 The solution is the point they cross at (1,-2)

Graph y = x -3 y = x + 2 Y X Solution= none

infinitely many solutions IDENTIFYING THE NUMBER OF SOLUTIONS NUMBER OF SOLUTIONS OF A LINEAR SYSTEM y x y x y x Lines intersect one solution Lines are parallel no solution Lines coincide infinitely many solutions

Name the Solution

Name the Solution

Name the Solution

Systems of Equations Solving by Graphing