Objective Students will choose the best method to solve linear
systems of equations
Slide 3
Before we begin Thus far we have looked at 3 different ways to
solve systems of linear equations This lesson focuses on you
choosing the best method given some guidelines Even though you can
solve each of the linear systems with each methodthe goal here is
for you to find the quickest, simplest way
Slide 4
Guidelines Recall that in the Graphing Method you transformed
the equations to slope-intercept form and graphed the lines. The
point where the lines intersect represents the solution to the
system of equations This method is useful for approximating a
solution, checking the reasonableness of a solution and providing a
visual model
Slide 5
Guidelines Recall that in the Substitution Method you solved
one of the equations for one of its variables and then substituted
the resulting expression into the other equation to get an equation
with one variable. You then solved the equation and used the result
to find the value of the other variable. This method is useful when
one of the variables has a coefficient of 1 or -1.
Slide 6
Guidelines Recall that in the Combination Method you
manipulated the equations to eliminate one of the variables. You
then combined the equations, solved for the variable and used the
result to determine the value of the other variable. This method is
useful when none of the variables have a coefficient of 1 or
-1.
Slide 7
Examples At this point lets look at some examples and see if we
can analyze them and determine the best method to solve based upon
the guidelines
Slide 8
Example #1 x + y = 300 x + 3y = 18 Take a minute and look at
the guidelines and see if you can determine the best method. You
should be able to explain your choice In this example you could
either use the substitution method or linear combinations. It would
be easy to write either variable in terms of the other or to
eliminate x by multiplying either equation by -1
Slide 9
Example #2 3x + 5y = 25 2x 6y =12 Again, look at the guidelines
and see if you can determine the best method. You should be able to
explain your choice In this example linear combinations would be
the best way to solve the equations since neither variable has a
coefficient of 1 or -1.
Slide 10
Example #3 2x + y = 0 x + y = 5 One more timeuse the guidelines
and see if you can determine the best method In this example any of
the three methods could be used. It would be simple to write either
variable in terms of the other, both would be simple to graph, and
y could be eliminated by multiplying either equation by -1
Slide 11
Comments The beauty of systems of equations is that you get to
choose what method you are most comfortable with. The key is to
analyze the equations first, then decide which method would be
easiest and quickest and then follow through using the steps you
learned.
Slide 12
Comments On the next couple of slides are some practice
problemsThe answers are on the last slide Do the practice and then
check your answersIf you do not get the same answer you must
question what you didgo back and problem solve to find the error If
you cannot find the error bring your work to me and I will
help
Slide 13
Your Turn Choose a method to solve the linear system. Explain
your choice. (You do not have to solve these problems) 1.6x + y = 2
9x y = 5 2.2x + 3y = 3 5x + 5y = 10 3.2x 5y = 0 x y = 3 4.3x + 2y =
10 2x + 5y = 3
Slide 14
Your Turn Choose a method and then solve 1.2x + y = 5and x y =
1 2.3x + 6y = 8and-6x + 3y = 2 3.8x + y = 15and9 = 2y + 2x 4.100 9x
= 5yand0 = 5y 9x 5.X + 2y = 2andx + 4y = -2 6.0.2x 0.5y = -3.8and
0.3x + 0.4y = 10.4
Slide 15
Your Turn Solutions Answers can vary. Make sure that you
explain your reasoning! 1.Substitution method 2.Linear combinations
3.Substitution or graphing method 4.Linear combinations 5(2, 1)
6(4/15, 1 1/5) 7(1 , 3) 8(5 5/9, 10) 9(6, -2) 10(16, 14)
Slide 16
Summary A key tool in making learning effective is being able
to summarize what you learned in a lesson in your own words In this
lesson we talked about applications of linear systems. Therefore,
in your own words summarize this lessonbe sure to include key
concepts that the lesson covered as well as any points that are
still not clear to you I will give you credit for doing this
lessonplease see the next slide
Slide 17
Credit I will add 25 points as an assignment grade for you
working on this lesson To receive the full 25 points you must do
the following: Have your name, date and period as well a lesson
number as a heading. Do each of the your turn problems showing all
work Have a 1 paragraph summary of the lesson in your own words
Please be advised I will not give any credit for work submitted:
Without a complete heading Without showing work for the your turn
problems Without a summary in your own words