Transcript Section 3.2 - Souderton Math

3.2 Solving Systems by Elimination
Objective:
Solve a system of two linear
equations in two variables by
elimination.
Standard:
2.8.11.H. Select and use an
appropriate strategy to solve
systems of equations.
1.
I. Elimination Method
The elimination method involves multiplying
and combining the equations in a system in
Arrange each equation so they are in the same form.
order to eliminate a variable.
2. Choose to eliminate either x or y.
3. If the coefficients of the variable you chose to eliminate
are different, multiply one or both equations to make the
coefficients the same size but opposite sign.
4. Add the like terms of the equations
5. Use substitution to solve for the remaining variable.
I. Independent Systems
Ex 1. Use elimination to solve the
system. Check your solution.
2x + y = 8
x – y = 10
Ex 2. Use elimination to solve the
system. Check your solution.
2x + 5y = 15
–4x + 7y = -13
Use elimination to solve the
system. Check your solution.
4x – 3y = 15
8x + 2y = -10
Ex 2.
This table gives production costs and selling
prices per frame for two sizes of picture frames.
How many of each size should be made and
sold if the production budget is $930 and the
expected revenue is $1920?
Production
Cost
Small
$5.50
Large
$7.50
Total
$930
$12
$15
$1920
Selling
Price
5.5x + 7.5y = 930
12x + 15y = 1920
* Multiply by -2
-11x – 15y = -1860
12x + 15y = 1920
x= 60 small
y = 80 large
II. Dependent and Inconsistent Systems
Ex 1. Use elimination to solve the system. Check your
solution.
2x + 5y = 12
2x + 5y = 15
** Multiply by – 1 to first equation
-2x – 5y = -12
2x + 5y = 15
0=3
Empty Set
Inconsistent
Parallel Lines (both equations have a slope of -2/5)
II. Dependent and Inconsistent Systems
Ex 2. Use elimination to solve the system. Check your
solution.
-8x + 4y = -2
4x – 2y = 1
-8x + 4y = - 2
8x - 4y = 2
Multiplied by 2
0=0
∞ Consistent Dependent
Use elimination to solve the system. Check your
solution.
1. 5x - 3y = 8
10x – 6y = 18
3. 4y + 30 = 10x
5x – 2y = 15
2. 6x – 2y = 9
6x – 2y = 7
4. 5x + 3y = 2
2x + 20 = 4y
Writing Activities
Homework
Integrated Algebra II- Section 3.2 Level A
Honors Algebra II- Section 3.2 Level B