1. 11.3 Solving Linear Systems by Adding or Subtracting

2. Solving Linear Systems * Graphing * Substitution
Today
Elimination or
(Linear Combinations)

3. Solving by Elimination
Line up the variables
Add or subtract to eliminate a variable
Solve for the remaining variable
Substitute into one of the original equations to find the second variable
CHECK in the opposite equation.

4. Solve the system: 3𝑥+4𝑦=8 −3𝑥+5𝑦=10
Are the variables lined up?
Add to eliminate a variable y = 18
Solve for y y = 2
Substitute y = 2 in original equation
3x + 4(2) = 8
3x + 8 = 8
3x = 0
x = 0
5. Check. -3(0) + 5(2) = 10
The solution is
(0, 2).

5. Solve the system:
3x + 4y = 8
-3x + 5y = 10

6. Solve the system:
5x + 6y = 4
7x + 6y = 8

7. Solve the system:
3x – 3y = 18
3y = -7x + 30

8. Let: b = speed of boat in still water c = speed of current
A riverboat travels 28 miles upstream in 7 hrs. It travels 28 miles downstream in 5 hrs. The speed of the current remains the same during the travel upstream and downstream. Find the average speed of the riverboat in still water and the speed of the current.
Let: b = speed of boat in still water
c = speed of current
Upstream: b + c =
Downstream: b – c =

9. A business center charges a flat fee to send faxes plus a fee per page
A business center charges a flat fee to send faxes plus a fee per page. You send one fax with 4 pages for $5.38 and another fax with 7 pages for $ Find the flat fee and the cost per page to send a fax.

10. Homework Page 497 #7, 9, 13, 17, 24 Page 509 #2-22 even, 25
Math + homework =
Math – homework =
Homework
Page 497 #7, 9, 13, 17, 24
Page 509 #2-22 even, 25