Section 1.3: APPLICATIONS OF SYSTEMS OF LINEAR EQUATIONS
When you are done with your homework you should be able to…
 Set up and solve a system of equations to fit a polynomial function to a set
of data points
 Set up and solve a system of equations to represent a network
POLYNOMIAL CURVE FITTING
Suppose n points in the xy-plane
represent a collection of ___________ and you are asked to find a
_______________________________ function of degree ___________
whose graph passes through the specified points. This procedure is called
_______________________ _______________ ____________________.
If all x-coordinates are distinct, then there is precisely _______ polynomial
function of degree n – 1 (or less) that fits the n points. To solve for the n
_____________________ of
p  x  , __________________ each of the n
points into the polynomial function and obtain n _________________ equations
in ____ variables a0 , a1 , a2 , , an 1 .
a0  a1 x1  a2 x12   an 1 x1n 1  y1
a0  a1 x2  a2 x2 2   an 1 x2 n 1  y2
a0  a1 x3  a2 x32   an1 x3n 1  y3

a0  a1 xn  a2 xn 2   an 1 xn n 1  yn
Example 1: Determine the polynomial function whose graph passes through the
points, and graph the polynomial function, showing the given points.
 2, 4  ,  3, 4  ,  4, 4 
Example 2: The table shows the U.S. population figures for the years 1940, 1950,
1960, and 1970. (Source: U.S. Census Bureau)
Year
1940
1950
1960
1970
Population
(in millions)
132
151
179
203
a. Find a cubic polynomial that fits these data and use it to estimate the
population in 1980.
b. The actual population in 1980 was 227 million. How does your estimate to
compare?
NETWORK ANALYSIS
Networks composed of ___________________ and __________________ are
used as models in fields like economics, traffic analysis, and electrical engineering.
In a network model you assume that the total _____________ into a
_________________ is equal to the total flow _____________ of the junction.
Example 3: The figure shows the flow of traffic through a network of streets.
x1
400
x2
x3
600
x4
300
100
x5
a. Solve this system for xi , i  1, 2, ,5 .
b. Find the traffic flow when x3  0 and x5  100 .
c. Find the traffic flow when x3  x5  100 .