warm up. lesson 67: solving and classifying special systems of equations expressions and equations
TRANSCRIPT
WARM UP
1. A(n) _________________ of linear equations is a set of linear
equations with the same variables.
2. Find the slope and y-intercept:
3. Find the slope and y-intercept:
4. Find the slope of a line parallel to .
5. Find the slope of a line perpendicular to .
VOCABULARY
Inconsistent Systems: systems of equations with no solution Graphically, these are parallel lines…they never cross Algebraically we will end up with an equality that is not true, such as 6=2
Consistent Systems: systems of equations that have at least one solution This includes independent systems and dependent systems
Dependent Systems: systems of equations with infinitely many solutions Graphically these are two equations for the same line Algebraically we end up with an identity, such as 0=0 or 12=12
Independent Systems: systems of equations with exactly one solution Graphically, these are two lines that cross at one point, like the systems we have talked about before
Algebraically, we will end up with one ordered pair that works for both equations
SYSTEMS OF LINEAR EQUATIONS
Systems of Linear EquationsConsistent and Independent
Consistent and Dependent Inconsistent
Exactly one solution Infinitely Many Solutions No Solution
The graphed lines intersect at exactly one
point
The graphed lines are the same line. The line is the
solution.
The lines are parallel and don’t intersect.
EXAMPLE
Solve the system of equations and classify it as consistent and independent, consistent and dependent, or inconsistent:
YOUR TURN
Solve the system of equations and classify it as consistent and independent, consistent and dependent, or inconsistent:
EXAMPLE
Solve the system of equations and classify it as consistent and independent, consistent and dependent, or inconsistent:
YOUR TURN
Solve the system of equations and classify it as consistent and independent, consistent and dependent, or inconsistent:
EXAMPLE
Solve the system of equations and classify it as consistent and independent, consistent and dependent, or inconsistent:
YOUR TURN
Solve the system of equations and classify it as consistent and independent, consistent and dependent, or inconsistent:
EXAMPLE
Brandon started jogging at a rate of 4 miles per hour. After he jogged 1 mile, his friend Anton started jogging on the same path at a pace of 4 miles per hour. If they continue to jog at the same rate, will Anton ever catch up with Brandon?
YOUR TURN
An emergency road service company offers different plans to its customers. Plan X offers service calls for $22 each. Plan Y offers a lower rate of $40 per month with an additional charge of $12 for each service call. How many service calls would it take for Plan Y to cost the same as Plan X? Explain.
CORRECTING HOMEWORK
Be kind.
If the paper in front of you has no work shown, return it to its owner.
If the paper in front of you is not in pencil or black ink, return it to its owner.
If the paper in front of you is not complete, return it to its owner.
Remember you are filling out the score sheet for the person that you are correcting.
Be sure to write “C.B. ____________” with your name on the paper you graded and on the score sheet.