# Lesson: 6-3 Solving Systems by Substitution

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### Lesson Objective

SWBAT solve systems of equations by substitution.

### Lesson Plan

 Teacher: Hall Course:    8th Math Date: Jan 6, 2009 Objective:  SWBAT solve systems of equations using the substitution method Unit Title: 6 Objective Number: Materials: do now, cc, notebooks/texts, HW, EX Vocabulary: solution, system of equations, substitution Do now: Purpose of the do now:  xCumulative Review _____________ â–¡Activate Prior Knowledge â–¡Introduce Lesson â–¡Other ___________________ Total Recall / Hook: How will you transition from the Do Now into today’s objective? How will you tie your recall to the importance of today’s objective?   Example 1 – real world application of systems of equations How is this problem related to systems of equations? What are the two situations? What question would this problem then ask? (When will Mr. Miller catch up; when will they be tied, etc.) How do we solve a system of equations? One way is by graphing – today we are going to learn a way to solve systems without graphing – just using algebra! What is substitution? etc MENTAL MATH   Not today Agenda: Outline of your lesson Do now (5 ) Cranium Crunch (5 ) Review CC/DN (10) 4.      Mental Math (5 ) 5.      Hook (5 ) 6.      INM1 (5 ) 7.      GP1 (10 ) 8.      CFU1 (2 ) 9.      IP1 (10 ) 10. INM2 (5 ) 11. GP2 (10 ) 12. CFU2 (3 ) 13. IP2 (25 ) 14. Share (5 ) 15. Exit Ticket (10 ) 16. Closing (5 ) Intro to NM     Example 2: So we are going to look for places that we can combine the information from these two equations into one equation – and we can do this by substituting!   Replace y with 3x – because y is already solved for. Why can I do this? (because at the intersection the two y values must be the same!) Why didn’t we replace the x instead?   Now solve for x – what does this x represent? (the x value when the two equations are equal) Is this the solution – no, we need a coordinate pair – so plug x in and find the value of y.   How do we check our answer? (Plug x and y into both equations)   Example 3: What makes this more difficult? What is the easiest variable to solve for? (x because it has a coefficient of positive one) What’s the next step, etc.? What does this point represent? If we graphed these equations, what would we expect to see?   Now You Try: First two just like examples 1 and 2 Next two have zero and infinite solutions   After they try on their own, review answers on the board – then go over answers to C and D – these look like strange solutions… What do these mean? Why? ·         If it is a true statement, then they have an infinite amount of solutions (same line) ·         If it is a false statement, then they have zero solutions (parallel)   QUICK WRITE Key questions to ask during GP: (Question Script)  - IP 1    IP: page 263-264 #1-6 (all); 9, 11, 13, 23, 25, 31, 35, 36 Closure: How will you close the lesson?    Any strategies for finding what to substitute? When would this be a better method than graphing? When would graphing be a better method?   Share out answers from IP Exit ticket Assessment: How will you assess mastery of the objective?     Exit ticket Homework   6-3 Anticipated Challenges

Reflection: Start to have students identify why substituting is a good strategy for certain problems – maybe wven preview what types of problems substitution won’t work well for.

### Lesson Resources

 6 3 packet 1,151 6 3 HW 596 6 3 DN 418