Transcript Chapter 7 Power Point

Solving systems of linear equations
Entry Task 02/17/2011
• Get 7.1B and a piece of graph paper
• Get out 6.4 so I can check it for group points.
• Copy the below information onto a sheet of
paper.
Section 7.1
• Objective: Solve systems of linear equations
by graphing. Model a real life problem using a
linear system.
Entry Task 02/12/2013
Write the following vocabulary in your
math notebook
• A system of linear equations in two variables is
two linear equations with two variables.
• A solution of a system of linear equations in two
variables is an ordered pair (x,y) that satisfies
each equation in the system.
• If the two lines do not cross (parallel) then there is
no solution.
• If the two lines do cross there is one solution.
• If the two lines are the same the answer is all real
numbers {(x,y); x  R _ and _ y  R }
Et 02/05/2013 copy this down: Solving systems
of two linear Equations by graphing
• 1.) Solve each equation for y
• 2.) Graph each equation (use a ruler!)
• 3.) Find the point of intersection
• This is your solution
4.) Check your answer
• If the two lines do not cross (parallel) then there is
no solution.
• If the two lines do cross there is one solution.
• If the two lines are the same the answer is all real
numbers {(x,y); x  R _ and _ y  R }
Solving a system of linear equations by
elimination
• Step 1: make sure all of your variables are
lined up
• Step 2: make sure a variable will cancel out if
you add the equations; if not multiply
• Step 3: add the two equations
• Step 4: Solve for the remaining variable
• Step 5: find the other variable
• Step 6: write your answer in the form (x,y)
Example
• Solve the linear system.
{
 x y 1
2 x  y  2
Section 7.2
• Objective: Use substitution to solve a linear
system. Model a real life problem using a
linear system.
Solving a linear system by substitution
• Step 1: solve one of the equations for one of
its variables.
• Step 2: substitute the expression from step
one into the other equation and solve for the
other variable.
• Step 3: Substitute the value from step 2 into
the revised equation from step one and solve.
• Step 4: check the solution in each of the
original equations.
Example
• Solve the linear system.
{
 x y 1
2 x  y  2
• Step 1: solve for y in equation 1.  x  y  1
x
x
y  x 1
• Step 2: Substitute x  1 for y in equation 2 and solve
for x.
2 x  y  2
2 x  ( x  1)   2
3x  1  2
x  1
Example cont.
• Step 3: to find the value of y, substitute -1 for x in
the revised Equation 1.
y  x 1
y  1  1
y0
• Step 4: check that (-1,0) is a solution by substituting
-1 for x and 0 for y in each of the original equations.
• The solution is (-1,0)
Entry Task 02/24/2011
• Get out 7.2B so I can check it for group points.
• Solve the following system of equations using
substitution, if you need help look on page
405 in your book.
{
2 x  y   10
3x  y  0
Entry Task 02/25/2011
• Get out 7.2B so I can check it for group points.
• Complete 7.2 Standardized Test Practice
problems 1-7. You have 14 minutes.
• When finished get a book and worksheet 7.3B
and take notes for section 7.3 on the back of
the worksheet. 7.3B is due on Tuesday.
Entry Task 02/28/2011
• Get out 7.3B and prepare any questions you
may have.
• If you have no questions start working on
problems 1-12, and 19-25
• 13-18 will be extra credit.
Entry Task 03/01/2011
• Get out 7.3B to check for group points
• Do numbers 1 and 2 on 7.3 stp
• Get a book and open to page 360, start taking
notes.
Entry Task 03/02/2011
• Get out pg. 363 #1-6 to check for group points
• Get a book and on your homework paper, do
problem number 7 on pg. 363.
Section 7.6
• Objective: Solve a system of linear inequalities
by graphing. Use a system of linear
inequalities to model a real-life problem.
• Open your books to page 432
Entry Task 03/03/2011
• Get out pg. 435 # 1-8 to check for group
points
• Work on your homework and prepare any
questions you may have. If you are finished
start on pg. 435 #9-17, 34-35.
Entry Task 03/04/2011
• Choose one of the following:
– Work on missing work
– Take the Quiz.
• If you are not working you will have to take
the quiz.