| From Last Time (#80)
Boat & Current: In his motorboat, Nguyen travels upstream
at top speed to his favorite fishing spot, a distance of 36 miles, in
two hours . Returning, he finds that the trip downstream, still at
top speed, takes only 1.5 hours. Find the speed of Nguyen's boat
and the speed of the current
method from Sec 2:
 |
From Last Time (#80)
Boat & Current: In his motorboat, Nguyen travels upstream
at top speed to his favorite fishing spot, a distance of 36 miles, in
two hours. Returning, he finds that the trip downstream, still at
top speed, takes only 1.5 hours. Find the speed of Nguyen's boat
and the speed of the current.
 method
from Sec 1:
 |
| Linear Systems of Inequalities
We have seen that linear systems of equations can
have 0, 1, or ∞
solutions depending on whether the equations are parallel,
independent, or dependent (respectively).
Last time, we learned how to use the Elimination and Substitution
methods for solving systems of equations. Now, let's see how a
graphing calculator can be helpful for solving problems like these .
Solve the fol lowing system by hand and by using a calculator's Table
and Graph (Intercept) functions.
 |
Using a TI83+ Graphing Calculator
to Solve a System of Equations1. Solve
each equation for y.
2. Enter equations into the calculator's [Y=] menu.
Then, to Solve Using a Table of Values :
A. Press [2nd][TBLSET] to set the table's parameters.
B. Press [2nd][TABLE] to view the table.
C. Scroll through the table to find a common (x, y) pair.
Or, to Solve Using a Graph:
I. Press [GRAPH]
II. Use [Trace] to estimate the point of intersection by tracing
along the curve , or
III. Use [2nd][CALC][5: Intersect] to have the calculator find
the point of intersection (this uses a numerical technique
similar to Newton's method from Calculus). |
| Sec. 8.8: Linear Inequalities & Systems
On the first slide, you solved the system
Now instead suppose the system was:
How would you describe the solution set for this
system of
inequalities?
 |
Solving Inequalities
The solution set for a linear inequality or system of inequalities is
not
just a single point, it is an entire region re presenting an infinite
number
of (x, y) pairs that all satisfy the given inequalities.
To graph a single linear inequality in two
variables:
1. Draw the boundary (dashed, unless "or equal to" present)
2. Choose a test point not on the line.
3. Shade the appropriate region.
To solve a linear system of inequalities:
1. Graph each inequality (as above).
2. Find the intersection of the two regions of the in dividual
inequalities. This is the solution set of the system. |
| Examples 1. Solve the
linear system:
|
Examples
2. Solve the linear system:
|
Examples
3. Graph the solution set of the linear system:
 |
Problem Set #3 Linear Programming
You will read two pages of your text on your own (p. 48485),
write a summary of the procedure they are presenting there, and
select and solve two related HW problems.
Tips for reading mathematics:
1. Don't read too fast! Math packs a lot of information in
small packages. Take your time to let it sink in.
2. Don't read too slow! Don't get hung up on small or
confusing details at first. Make a note, then read ahead.
3. Do the examples, too. Work through examples along with
the book, making your own notes and trying steps on
your own .
4. Take a second look. Go back and reread
parts that you first found confusing after you have moved on.
5. Reflect & summarize. What's the big idea? How would you
explain it to your peers? Try making up your own examples to
test your knowledge. |
