| Algebra 1 Notes
Chapter Eight
Section 8.1
Section 8.2
Section 8.3
Section 8.4
Section 8.5
Section 8.6
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Section
8.2 The Substitution Method
(Examples provided by Prentice
Hall)
Part I: Substituting for a Variable
Solve.
| Example
1 |
|
| y
= 3x |
|
(1) |
| 2x
+ 4y = 28 |
(2) |
Use (1) to substitute for y in (2).
2x + 4(3x) = 28
2x + 12x = 28
14x = 28
x = 2
Substitution in (1) yields y = 3(2) = 6.
The solution (2, 6) checks. |
|
| Example
2 |
| 2x
+ y = 13 |
|
(1) |
| 4x
– 3y = 11 |
(2) |
Use (1) to solve for y in terms of x.
y = –2x + 13
Substitute in (2).
4x – 3(–2x + 13) = 11
4x + 6x – 39 = 11
10x = 50
x = 5
Substitution in (1) yields y = –2(5) + 13 = 3.
The solution (5, 3) checks. |
Part II: Problem Solving
Translate into a system of linear equations and solve.
| Example
1 |
|
The
sum of a number and twice another number is 13. The first number
is 4 larger than the second number. What are the numbers?
Let x be the first number. Let y be the second
number.
| x
+ 2y = 13 |
|
(1) |
| x
= y + 4 |
(2) |
Use (2) to substitute for x in (1).
(y + 4) + 2y = 13
3y = 9
y = 3
Substitute in (2), x = 3 + 4 = 7.
The solution (7, 3) checks. |
Take class notes.
Before starting your homework, rework the
examples that are illustrated in this section of your textbook and the
examples that I demonstrated in class.
Then do your homework.
Write down questions (examples or concept
that you do not understand).......then.............. Ask these questions
in class.
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