1. Systems of Equations
Solving by Graphing

2. 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.

3. 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)

4. 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)

6. Graph y = x y = x + 2 Y X
Solution= none

8. 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

9. Name the Solution

10. Name the Solution

11. Name the Solution

12. Systems of Equations
Solving by Graphing