7-1 Graphing Systems of Equations SWBAT: 1) Solve systems of linear equations by graphing 2)...
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Transcript of 7-1 Graphing Systems of Equations SWBAT: 1) Solve systems of linear equations by graphing 2)...
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)