(b)x= 5
180 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions
xy
2
6
3xy
5 2
5 6
5 3Ordered Pairs1 5, 3 21 5, 6 21 5, - 22The given equation
is No matter
which value of yis
chosen, the value of
xis always 5.
x=5.
NOW TRYNOTE We can think of in Example 4(b)as an equation in two variables by
rewriting as This form of the equation shows that, for any value
of y, the value of xis 5. Similarly, y= 4 can be written 0 x+ y= 4.
x= 5 x+ 0 y=5.
x= 5
OBJECTIVE 6 Plot ordered pairs. In Section 2.3,we saw that linear equations
in onevariable had either one, zero, or an infinite number of real number solutions.
These solutions could be graphed on onenumber line. For example, the linear equa-
tion in one variable has solution 7, which is graphed on the number line
in FIGURE 2.
x- 2 = 5
0 7
FIGURE 2Every linear equation in twovariables has an infinite number of ordered pairs
as solutions. To graph these solutions, we need twonumber lines, one for each
variable, drawn at right angles as in FIGURE 3. The horizontal number line is called
the x-axis,and the vertical line is called the y-axis.The point at which the x-axis
and y-axis intersect is called the origin.Together, the x-axis and y-axis form a
rectangular coordinate system.
The rectangular coordinate system is divided into four regions, called quadrants.
These quadrants are numbered counterclockwise, as shown in FIGURE 3.
1 x, y 2
xy- 624 –4 6
–2
–4
–6
246–2 0Quadrant III Quadrant IVQuadrant II Quadrant I
Originy–axisx–axisFIGURE 3Rectangular Coordinate SystemRené Descartes (1596–1650)
The rectangular coordinate system
is also called the Cartesian
coordinate system,in honor of
René Descartes, the French
mathematician credited with
its invention.
The x-axis and y-axis determine a plane—a flat surface illustrated by a sheet of
paper. By referring to the two axes, we can associate every point in the plane with
an ordered pair. The numbers in the ordered pair are called the coordinatesof the
point.
NOW TRY
EXERCISE 4
Complete the table of values
for the equation. Write the
results as ordered pairs.
5 x- 4 y= 20
xy
0
0
2NOW TRY ANSWER
4.
1 0, - 52 , , 1 4, 0 (^2) A2, - 25 B
xy
0
40
2 -^52
- 5
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