1. Solving Systems of Equations by Graphing

2.  System of Equations- Two or more equations with the same variables  Consistent- A system of equations with at least one solution  Inconsistent- A system of equations with no solutions  Independent- A system of equations with exactly one solution  Dependent- A system of equations with an infinite number of solutions

3.  Three choices: ◦ Consistent and Independent ◦ Consistent and Dependent ◦ Inconsistent  Must have both equations in y=mx+b to classify

4.  Where the lines in the system intersect each other

5.  Two intersecting lines  One solution  Different slopes

7.  Same line  Infinitely many solutions  Same slope and same y-intercept

9.  Parallel lines  No solution  Same slope, different y-intercepts

11.  Graph each equation on the graph  Where the lines intersect is the solution  Solution written as an ordered pair (x,y) ◦ If there are infinitely many solutions, write it as such

15. xY 1 (from one equation) Y 2 (from other equation) -2F 1 (-2)F 2 (-2) F 1 (-1)F 2 (-1) 0F 1 (0)F 2 (0) 1F 1 (1)F 2 (1) 2F 1 (2)F 2 (2) 3F 1 (3)F 2 (3) Plug value for x into each equation to get a value for y Use more x values until you find one where you get same y value for both equations

16.  Y=2x+9  Y=-x+3 xY=2x+9Y=-x+3 -2 0 1 2 3

17.  x + y = 4  -4x + y = 9 xx+y=4-4x+y=9 -2 0 1 2 3

18.  Turn Calculator on  Press Y= button on top left  In Y 1 = plug in first equation  In Y 2 = plug in second equation  Top right button GRAPH  Press 2 nd button, below y=, then press TRACE button  Select option 5:intersect  Press enter 3 times  Enter answer as ordered pair

19.  Press WINDOW button, right of y=  Standard viewing window should be as follows: ◦ Xmin=-10 ◦ Xmax=10 ◦ Xscl=1 ◦ Ymin=-10 ◦ Ymax=10 ◦ Yscl=1

20.  If you can’t see the intersection, change the viewing window  Press WINDOW button, right of y= button  If you need to see farther up the graph, increase the Ymax  If you need to see farther down on the graph, decrease the Ymin  If you need to see farther right on the graph, increase the Xmax  If you need to see farther left on the graph, decrease the Xmin

22.  Worksheet 3-1