WARM UP

LESSON 67: SOLVING AND CLASSIFYING SPECIAL SYSTEMS OF EQUATIONS Expressions and Equations

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 Equations Consistent and IndependentConsistent and DependentInconsistent Exactly one solutionInfinitely Many SolutionsNo 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

YOUR TURN

EXAMPLE

YOUR TURN

EXAMPLE

YOUR TURN

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.

HOMEWORK QUESTIONS

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.

HOMEWORK  1 st and 2 nd hour: Lesson 67 a-e, #7-9, 11, 13, 14,  3 rd hour: Lesson 67 a-e, 7, 8, 13, 19, 22, 26-30