1. Write a system of equations. Let x represent
Example 3
Write and solve a linear system
SOCCER
A sports equipment store is having a sale on soccer balls. A soccer coach purchases 10 soccer balls and 2 soccer ball bags for $155. Another soccer coach purchases 12 soccer balls and 3 soccer ball bags for $189. Find the cost of a soccer ball and the cost of a soccer ball bag.
SOLUTION
Write a system of equations. Let x represent
the cost of a soccer ball, and let y represent
the cost of a soccer ball bag.
STEP 1

2. Equation 1: Purchase by first soccer coach
Example 3
Write and solve a linear system
Equation 1: Purchase by first soccer coach
x y • + =
Equation 2: Purchase by second soccer coach
x y • + =

3. STEP 2 Multiply Equation 1 by 3 and Equation 2 by 2
Example 3
Write and solve a linear system
STEP 2 Multiply Equation 1 by 3 and Equation 2 by 2
so that the coefficient of y in each equation
is the least common multiple of 3 and 2, or 6.
10x y + =
12x y
30x y
24x y  3 2
STEP 3 Subtract the equations. 6x =
STEP 4 Solve for x. x =

4. STEP 5 Substitute 14.5 for x in either of the original
Example 3
Write and solve a linear system
STEP 5 Substitute 14.5 for x in either of the original
equations and solve for y.
Write Equation 1.
10x y + =
Substitute 14.5 for x. y + = ( )
14.5
Solve for y. y =
ANSWER
A soccer ball costs $14.50, and a soccer ball bag costs $5.

5. 10 yd of quilting fabric and 6 yd of sateen
Guided Practice
for Example 3 7.
FABRIC
Dina makes a quilt that has alternating stripes of quilting fabric and sateen fabric. Quilting fabric costs $4 per yard, and sateen fabric costs $6 per yard. She spends $76 on a total of 16 yards of the two fabrics. Find the amounts of quilting fabric and sateen fabric that Dina purchases.
ANSWER
10 yd of quilting fabric and 6 yd of sateen