OBJECTIVE 1 Solve geometry problems by using two variables.
Finding the Dimensions of a Soccer Field
A rectangular soccer field may have a width between 50 and 100 yd and a length
between 100 and 130 yd. One particular soccer field has a perimeter of 320 yd. Its
length measures 40 yd more than its width. What are the dimensions of this field?
Step 1 Readthe problem again. We are asked to find the dimensions of the field.
Step 2 Assign variables.Let L=the length and W= the width. See FIGURE 8.
EXAMPLE 1
234 CHAPTER 4 Systems of Linear Equations
Solving an Applied Problem by Writing a System of Equations
Step 1 Readthe problem, several times if necessary. What information is
given? What is to be found? This is often stated in the last sentence.
Step 2 Assign variablesto represent the unknown values. Use a sketch,
diagram, or table, as needed.
Step 3 Write a system of equationsusing the variable expressions.
Step 4 Solvethe system of equations.
Step 5 State the answerto the problem. Label it appropriately. Does it
seem reasonable?
Step 6 Checkthe answer in the words of the originalproblem.
The following steps are based on the problem-solving method of Section 2.3.
L
W
FIGURE 8
Step 3 Write a system of equations.Because the perimeter is 320 yd, we find one
equation by using the perimeter formula.
We write a second equation using the fact that the length is 40 yd more than
the width.
These two equations form a system of equations.
(1)
L= W+ 40 (2)
2 L + 2 W= 320
L =W+ 40
2 L+ 2 W= 320 2 L+ 2 W=P
