Graphing Method
Solve the following system of equations by graphing. Identify the number of solutions; One, (write answer as an ordered pair) None, or Infinite and why? y=3x-4 y=3x-4
Answer: No Solution because the slopes are the same. Therefore, the lines are parallel.
3x+9y=-18
y= -3x-2
If both equations in a system have the different slopes how many solution exist to the equations?
One solution
The graph of a system of equations with one solution
The pair of lines cross at one point (two intersecting lines at one point)
6x+3y=9
y=-2x+3
Fill in the blank. The point of intersection is the same as the __________ to a system of equations.
Solution
The graph of a system of equations with no solution
Parallel Lines
4x+2y=2
Answer: y=-2x+1
If the slopes are the same but the y-intercepts are different, how many solutions are there? Why?
No solution because they don't intersect (they are parallel)
The graph of a system of equations with infinitely many solutions
Two overlapping lines
5x-y=8
y= 5x-8
Lines that have the same slope and y-intercepts have how many solutions?
Infinitely many solutions
y=2x-3
-6x+3y=-9
Infinitely many solutions
Solve the system by graphing:
-2x+2y=-16
3x-6y=30
(6, -2)
5x+4y=-12
Answer: y= -4/5x-3
Write a system of equations with no solution.
Answers vary. (Any linear equations with the same slope-parallel lines)
-3x+4y=12
-3x+4y=24
No solution (parallel lines)