This document discusses the substitution method for solving systems of equations. It provides two examples of using this method. The substitution method involves: (1) defining variables, (2) writing a system of equations, (3) substituting the value of one variable into another equation to eliminate that variable, (4) solving the resulting equation for the remaining variable, and (5) substituting this value back to find the first variable. This allows the system to be solved to find the values of both original variables.

1. ALGEBRAIC PROCESS
SYSTEM OF EQUATIONS

2. SUBSTITUTION METHOD EXAMPLES
 The perimeter of Mrs. McCord’s
rectangular garden is 100 feet. If the
length is 1.5 times longer than the width,
what are the dimensions of the garden?
a) Define the variables
 l= length
 w= width

3. b) Make the system of equations to
represent the problem
c) Look at the second equation in the
system, l=1.5w . How can this
information about l be used in the first
equation?
d) Because l=1.5w, substitute 1.5w in
place of l in the first equation. Solve
the new equation for w.

5. e) Substitute this value of w into the
second equation to find l.
f) Write a complete statement to answer
the question.
The garden is 20 feet width and 30 feet
long.

6. SUBSTITUTION METHOD
EXAMPLES
When a smaller number is subtracted
from a larger number, the difference is
34. If the larger number is 30 less than
3 times the smaller number, what are
the two numbers?
a) Define the variables
x: the larger number and
y: the smaller number
b) Write the system of equations.

7. c) Substitute the value of the second
equation in the first equation.

8. d) Substitute this value in the second
equation to find x.
e) The larger number is 66 and the
smaller number is 32.

9. SUBSTITUTION METHOD
 CONCLUSIONS:
a) There are at least two equations.
b) In the equations there are at least one variable.
c) Define the variables.
d) Use either equation to solve for one variable in
terms of the other.
e) Then calls for obtaining a third equation
involving only one variable to solve it.
f) To find the value of the other variable,
substitude the answer in any equation.

10. HOMEWORK
 Page 352 Exercises 2 to 14 even old book