Download Solving Systems Using Elimination Warm Up: Notes:

Algebra
Ch 6 Systems of Equations and Inequalities
Section 6.3 Notes
#3
Name____________________
Solving Systems Using Elimination
Warm Up:
Solve using substitution. Be sure that your final answer is an ordered pair, (x, y), and that
you circle your final answer.
1)
3)
y  x 1
x y 3
2)
x  4y  8
2 x  5 y  29
What two methods have we learned so far to solve system of equations?
Target Goal: Students will be able to solve systems of equations using the elimination method.
Notes:
Define: Elimination Method for solving a system of equations:
Steps to follow:
1. Line up the variables and constants.
2. Add down to eliminate one variable (you may need to multiply one
equation by –1 first)
3. Solve the resulting equation.
4. “Plug it in” to either original equation to solve
for the other coordinate.
5. Write the solution as an ordered pair.
6. Check that the solution makes both equations true.
Example 1) Use elimination to solve each system of equations.
a)
4 x  3 y  11
2 x  3 y  13
b)
3 x  4 y  12
3 x  6 y  18
Example 2) Use elimination to solve each system of equations.
a)
4 x  2 y  6
5 y  4 x  1
b)
4 x  3 y  11
 4 x  3 y  13
Elimination Method Using Multiplication: For some systems of equations, it is
necessary to multiply one or both of the equations by a different number in order to get one of
the variables to eliminate.
Example 3) Use elimination to solve each system of equations.
a)
2x  5 y  3
 x  3 y  7
b)
c)
2x  5 y  3
4 x  10 y  6
d)
2x  y  1
5x  3 y  2
3 x  3 y  6
2 x  y  2
ASSIGNMENT: #3 – Worksheet 6.3