Solving Systems of Equations by Graphing
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
Three choices: ◦ Consistent and Independent ◦ Consistent and Dependent ◦ Inconsistent Must have both equations in y=mx+b to classify
Where the lines in the system intersect each other
Two intersecting lines One solution Different slopes
Same line Infinitely many solutions Same slope and same y-intercept
Parallel lines No solution Same slope, different y-intercepts
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
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
Y=2x+9 Y=-x+3 xY=2x+9Y=-x
x + y = 4 -4x + y = 9 xx+y=4-4x+y=
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
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
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
Worksheet 3-1