1. Indicator 16
System of Equations

2. Two or more linear equations form a system of linear equations.
Any ordered pair that makes ALL of the equations in a system true is a solution.

3. Method 1: Graphing
Graph each equation on the same coordinate plane and find the intersection point.
A system of equations that has at least one solution is consistent.
A consistent system that has exactly one solution is independent.
A consistent system that is dependent has infinitely many solutions.
A system of equations that has no solution is inconsistent.

4. Example 1
Solve each system by graphing.
y=-x+6
y=3x+2

5. Example 2
Solve each system by graphing.
y=4x+3
y=-x-2

6. Example 3
Solve the system by graphing. State whether there is one solution, infinitely many solutions, or no solution.
3x+3y=12
2x+2y=4

7. Example 4
Solve each system by graphing. State whether there is one solution, infinitely many solutions, or no solution.
3x+y=2
4y=-12x+8

8. Example 5
Solve each system by graphing. State whether there is one solution, infinitely many solutions, or no solution.
3y-x=-9
x+y=1