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**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

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**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 • + =

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**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 =

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**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.

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**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

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3.5 Solving systems of equations in 3 variables

3.5 Solving systems of equations in 3 variables

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