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 .

LESSON 67: SOLVING AND CLASSIFYING SPECIAL

SYSTEMS OF EQUATIONSExpressions 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 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.

HOMEWORK QUESTIONS

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

1st and 2nd hour: Lesson 67 a-e, #7-9, 11, 13, 14, 16-30

3rd hour: Lesson 67 a-e, 7, 8, 13, 19, 22, 26-30