Chapter Eight

Chapter Eight: Systems of Equations

Take notes on the following topics.

Algebra 1 Notes

Chapter Eight

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Section 8.1 Solving Systems of equations by Graphing

Vocabulary:

A set of equations for which a common solution is sought is called a system of equations
A solution of a system of two equations in two variables is an ordered pair that makes both equations true.

(Examples provided by Prentice Hall)

Part I: Identifying Solutions

Determine if the given point is a solution of the system.

Example 1 Determine whether (3, 5) is a solution of the system.
y = 4x – 7
x + y = 8

y = 4x – 7

5 = 4(3) – 7

5 = 12 – 7

5 = 5 Ö

x + y = 8

3 + 5 = 8

8 = 8 Ö

(3, 5) is a solution.

Example 2 Determine whether (–2, 1) is a solution of the system.
2x – y = –5
3x + 2y = 3

2x – y = –5

2(–2) – 1 = –5

–4 – 1 = –5

–5 = –5 Ö

3x + 2y = 3

3(–2) + 2(1) = 3

–6 + 2 = 3

–4 = 3

(–2, 1) is not a solution of the system as it does not satisfy the second equation.

Part II: Finding Solutions by Graphing

Solve the system by graphing.

Example 1 x + y = 2 Check this equation with text.
x = y
A graph of the two lines indicates that they intersect at (1, 1). This point checks in the system.

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.