With regard to FIGURE 1, we can use a linear equation to model the graph of digi-
tal camera sales (the blue equation below) and another linear equation to model the
graph of digital camcorder sales (the red equation below).
210 CHAPTER 4 Systems of Linear Equations
OBJECTIVES In recent years, the sale of digital cameras has increased, while that of digital
camcorders has decreased. See FIGURE 1. The two straight-line graphs intersect at the
point in time when the two products had the samesales.
Systems of Linear Equations in Two Variables
4.1
1 Decide whether an
ordered pair is a
solution of a linear
system.
2 Solve linear systems
by graphing.
3 Solve linear systems
(with two equations
and two variables)
by substitution.
4 Solve linear systems
(with two equations
and two variables)
by elimination.
5 Solve special
systems.600080004000
2000Years since 2000
Source: Consumer Electronics
Association.0 2468Sales(in millions of dollars)Digital
camerasSmile!Digital camcordersFIGURE 1119 x+ y= 2838
624 x- y=- (^1823) (Here, represents 2000, represents 2001,
and so on; yrepresents sales in millions of dollars.)
x= 0 x= 1
; 1 4, 2 2
Such a set of equations is called a system of equations—in this case, a linear
system of equations.The point where the graphs in FIGURE 1intersect is a solution
of each of the individual equations. It is also the solution of the linear system of
equations.
OBJECTIVE 1 Decide whether an ordered pair is a solution of a linear
system. The solution set of a linear systemof equations contains all ordered pairs
that satisfy all the equations of the system at the same time.
Deciding Whether an Ordered Pair Is a Solution