Beginning Algebra, 11th Edition

CHAPTER 3 Summary^239

Is or a solution of

is not a solution. is a solution.

Complete the ordered pair for

Let

Multiply.

Subtract 4.

The ordered pair is 10 ,- 42.

• 4 =y

0 =y+ 4

3102 =y+ 4 x=0.

1 0, 2 3 x=y+4.

1 2,- 52 1 0,- 62

4122 - 31 - 52 = 23 Z 18 4102 - 31 - 62 = 18

1 2,- 52 1 0,- 62 4 x- 3 y=18?

QUICK REVIEW

(continued)

CONCEPTS EXAMPLES

3.1 Linear Equations in Two Variables;

The Rectangular Coordinate System

An ordered pair is a solution of an equation if it satisfies
the equation.

If a value of either variable in an equation is given, then
the other variable can be found by substitution.

Plot the ordered pair by starting at the origin,
moving 3 units to the left, and then moving 4 units up.

1 - 3, 4 2

3.2 Graphing Linear Equations in Two

Variables

To graph a linear equation, follow these steps.

Step 1 Find at least two ordered pairs that satisfy the
equation.

Step 2 Plot the corresponding points.

Step 3 Draw a straight line through the points.

The graph of passes through the origin.
Find and plot another point that satisfies the equation.
Then draw the line through the two points.

The graph of is a horizontal line through

The graph of xkis a vertical line through 1 k, 0 2.

yk 1 0,k 2.

AxBy 0

0 x

y

(–3, 4 )

Up 4Left 3

0

x=–3

x

y

y=–3

xy

0

40

• 2

0

2 x + 3y=0

(3, –2)

x

y

(0, 0)

0

x – 2y=4

(4, 0)

(0, –2)

x

y