Chapter Eight

Chapter Eight: Systems of Equations

Take notes on the following topics.

Algebra 1 Notes

Chapter Eight

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Section 8.3 The Addition Method

(Examples provided by Prentice Hall)

Part I: Using the Addition Method

Solve.

Example 1

2x + 3y = 11 (1)

–2x + 9y = 1 (2)

Add (1) and (2) to get
0 + 12y = 12
12y = 12
y = 1
Substitute in (1).
2x + 3(1) = 11
Solve for x.
2x = 8
x = 4
The solution (4, 1) checks.

Part II: Using the Multiplication Property First

Solve.

Example 1

5x + 3y = 22     (1)

5x + 6y = 34 (2)

Multiply (2) by –1 to get –5x – 6y = –34.
Add to equation (1).
0 – 3y = –12
y = 4
Substitute in (1).
5x + 3(4) = 22
5x = 10
x = 2
The solution (2, 4) checks.

Example 2

–6x + 5y = 4     (1)

3x + 4y = 11 (2)

Multiply (2) by 2 to get 6x + 8y = 22. Now add this to (1).
0 + 13y = 26
y = 2
Substitute in (1).
–6x + 5(2) = 4
–6x = –6
x = 1
The solution (1, 2) checks.

Example 3

2x + 3y = 23     (1)

3x + 5y = 37 (2)

Multiply equation (1) by 3, and equation (2) by –2 to get

6x + 9y = 69     (1)

–6x – 10y = –74 (2)

Add.
0 – y = –5
y = 5
Substitute in (1).
2x + 3(5) = 23
2x = 8
x = 4
The solution (4, 5) checks.

Part III: Problem Solving

Solve.

Example 1 Four times a certain number is three more than twice another number. The sum of the first number and twice the second number is 5. Find the numbers.

Let x be the first number and let y be the second number.

4x = 2y + 3 (1)

x + 2y = 5 (2)

When the first equation is written in standard form the system becomes

4x – 2y = 3 (1)

x + 2y = 5 (2)

Add.
5x = 8
x = 8/5
Substitute in (2).
(8/5) + 2y = 5
Solve for y.
2y = 17/5
y =17/10
The solution is (8/5, 17/10).

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.