1. 1. 2x + 2y = 6 2. x - y = - 1 3. 3x + y = - 3 4. -2x + 2y = - 2
Warm - Up
Graph each equations on its own coordinate plane.
1. 2x + 2y = 6
2. x - y = - 1
3. 3x + y = - 3
4. -2x + 2y = - 2

2. Solve a system of linear equation in two variables
The Graphing Method
A System of equations is two equations with the same two variables.
To Solve a system of equation we find values of the variables that are common to both equations.
An easy way to find a solution is to graph both equations on the same coordinate plane
and look for solutions that are common (the place where the graphs intersect).
Three situations can arise when solving a system.
1. The lines cross and we have a solution.
(consistent or independent system)
2. The lines are parallel and never cross so there is no solution.
(inconsistent system)
3. The lines may be the same and have an infinite amount of solutions.
(dependent system)

3. Solve a system of linear equation in two variables
The Graphing Method
Examples
Graph each pair of equations on a single coordinate plane.
1. 2x + 2y = 6
2. x - y = - 1
(answer: (1, 2))
3. 3x + y = - 3
4. -2x + 2y = - 2
(answer: (-1/2, -3/2))

4. Solve a system of linear equation in two variables
The Graphing Method
Practice
Determine all of the solutions for the following system of equations.
(answer: (-2, 3))
(answer: infinite solutions)
(answer: no solution)
(answer: (-3, -2))

5. Describe the three possible outcomes when graphing
Solve a system of linear equation in two variables
The Graphing Method
Journal
Describe the three possible outcomes when graphing
two lines on one coordinate plane.
Include definitions and graphs.