7.3 Solving by Elimination

Hope you all worked hard on your quiz today.  My apologies for not being there.

As we move into solving systems of linear equations through elimination, it's important you track the signs of our terms.  Mistakes with negatives will make solving by elimination difficult.  If you need any additional practice (extra credit) with integer work, please let me know.

Please start by watching an overview of what solving linear equations through elimination is:

Solving Linear Equations by Elimination - Overview

Then, watch the videos for each section and do the related problems (#* done in video):

Solving Linear Equations by Elimination - Addition #4

HW: pg 394 #s 3, 4*, 5

Solving Linear Equations by Elimination - Subtraction #12

HW: pg 394 #s 12*, 13, 14

Solving Linear Equations by Elimination - Arrange & Add/Subtract #22

HW: pg 394 #s 22*, 23, 24

7.1 & 7.2 Quiz Tomorrow

Just reminding you that I have moved our quiz from Thursday to tomorrow.  It will not include "elimination" as a method for solving systems of linear equations.

Please be sure to do the Practice Quiz - Homework.  I am attaching videos below of the solutions for those problems.  My suggestion would be to watch the video after you attempt the homework similar to how we did the Practice Quiz - Classwork in class today.

Videos of Solutions to Practice Quiz - Homework

1. translating into algebra
2. solving systems of equations by graphing
3. solving systems of equations by substitution

If you still have questions, please feel free to email me:

jadams@a-cs.org

Good luck tomorrow!

7.2 Solving Linear Equations Word Problems through Substitution

Hope you all had a good weekend.  Your homework was to watch the video in the last post.  I know we're not supposed to give homework on weekends but this seemed pretty important;)

Anyway, I'm hoping you are feeling confident with solving linear equations by graphing.  It's a lot of work but the goal was to see how all the tools: grids, equations, tables & graphs interrelate.  

As we've begun work on solving systems of linear equations I've gotten a resounding, "Wow, this is so much quicker!"  True, but we still want to maintain a conceptual understanding of the conceptual process of finding a shared solution point.

Accordingly, your homework will include translation tasks (words to algebra) and two word problems.

Please watch this video of me solving #16 on your homework and then complete the following:

HW: pg 386 #s 8, 14, 15, 16

Then answer:

HW: pg 387 #s 25 & 26 (pay close attention to "The value of x is 4 times the value of y"
                                     as you might write this as 4x = y which is incorrect.)

Watch the second video of me solving #29 starting with a grid and then using substitution (instead of tables & graphs) once I have the equations set up.  Write down the notes from my work on # 29 and then solve your own word problem #30 using a grid to make your equations and then substitution.

HW: pg 387 #s 29 & 30

Kid Snippets: "Math Class" (Imagined by Kids)

7.2 Systems of Equations & Start of Solving by Substitution

We will wrap up some practice constructing systems of linear equations from word problems.  A hard part can be learning to translate English into Algebra and vice-versa. 

An example would be:

     Small cards cost $3 each and large cards cost $5 each.  The total amount from the
     sale of the cards is $95. 

     We can choose to make:
     x = the number of small cards sold and 
     y = the number of large cards sold.

     In this scenario 3x + 5y = 95 means $3 per small card plus $5 per large card adds up to

     a total of $95 dollars.  

     There are multiple ways of solving this first equation.  It's only when we say the total
     number of cards is 25, translated to x + y = 25 that we have a systems of equations
     with one common answer.

     In this scenario x + y = 25 translates to "the number of small cards plus the number of
     large cards is 25 cards.  Note that cost is not associated with this function.

HW: pgs 380-81 #s 31, 32, *36 (*do a grid/table/equation/graph for 36)

Today, we will also begin solving linear systems by substitution.  Please watch the following videos of me solving #3 & #4 from your HW, copy the work and answers down, and do the remaining HW problems:

AND HW: pg 386 #s 3-7

7.2 Solving Linear Systems by Substitution - Page 386, #3 - part 1

7.2 Solving Linear Systems by Substitution - Page 386, #3 - part 2
7.2 Solving Linear Systems by Substitution - Page 386, #4

7.1 Suggestions for Long-Term Success in Math

I was one of those students that had it pretty easy in math until about the time of algebra.  I could tune out the teacher most of the time and "figure out" the math I was required to do.  On some level I even passed through Algebra pretty well.

Unfortunately, instead of developing the tools I needed to succeed long-term in math I continued to look for quicker, easier ways of doing math.  By the time I got into Calculus my ability to just "figure out" math was not longer working.  I had not developed the problem-solving and reasoning I needed to continue into advanced mathematics.

Here are some simple (but time-consuming) suggestions:

• watch the videos at least once (jump ahead if it seems slow, review if you're uncertain)
• show all your work (done in columns so you can more easily track errors with negatives)
• check your answers (especially if the instructions ask you to)
• use our tools of algebra to help you:
• a grid for word problems
• a function table (x,y) with labels
• a graph with labels
• the function written as a linear equation (y=mx+b)

I'll quiz you tomorrow on these as an extra credit you can apply later.

Today, please watch the video of me solving question #3 on your homework.

HW: Practice Sheet 7.1, #s 1-4 
(For question #4, feel free to substitute non-blooming annuals cost $1.60 and the total for 24 plants is $48.)

7.1 Nice job! Now going deeper into systems of equations with word problems.

Well done on your quizzes last week!  I observed that a number of you took the time to use all three tools (function, table & graph) to solve the word problems on quiz.  Your process is getting stronger as you make mistakes, catch them and continue to work hard on your conceptual understanding of what you are doing.

You may be starting to realize that algebra is getting rather time-consuming.  This week there will be even more steps to solve our assigned tasks. As it gets more complicated it is important you understand what you are doing and why so you can remember the process for solving systems of equations.

Chapter 7 - Section 1
Basically we are combining the questions you answered on your quiz.  You will be solving word problems that have 2 linear equations instead of just one linear equation.

If this seems totally new to you, please review the videos from last week:

page 378 - Example 3
grid
function/equation
graph/table/solution

If you feel you're ready to try a more difficult problem, go to these videos:

page 380 - #34
grid
table/graph
function/solution

HW: pg 379-81 #s 18, 20, 30, 37 (show function/table/graph)