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 slopeThey 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)