7-1 Graphing Systems of Equations SWBAT: 1) Solve systems of linear equations by graphing 2) Determine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent

What is a System of Equations? A system of equations is two or more equations with the same variables The solution to a system of equations is the ordered pair that is a common solution of all the equations One way we can solve a system of equations is by graphing the equations on the same coordinate plane

Lets Look at our Packet… They intersect at (2,4), and both have it as a solution.

Look at another… So they both have (- 1,4) as a solution.

One more! y = 4/3 x - 4 y = 2/3 x - 6 So they both have (-3,- 8) as a solution.

Consistent and Independent When two lines intersect, a system of equations has one solution (meaning only one point will satisfy the system). When a system has one solution, the system is said to be consistent and independent.

Wait…What About? These two lines are parallel! They have same exact slope They will never cross!

Inconsistent This would occur if the equations never intersect (they are parallel). They have no common coordinates. When a system of equations has no solution, the system is said to be inconsistent.

What happens here? y = -5x - 2 These two lines the same equation! They are the same exact line!

Consistent and Dependent This would occur if the equations are the same exact line. All the coordinates are the exact same. So there are infinite solutions. When a system of equations has infinitely many solutions, the system is said to be consistent and dependent.

Summary…

Example 2: Solve the system of equations by graphing. Then describe the solution.

b)

c)