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Example 4 A National Hockey League team receives 2 points for each win (in regulation time or overtime), 1 point for each loss in overtime, and no points for each loss in regulation. There are no ties. One season, the Los Angeles Kings lost 35 games in regulation. Use the table to find the number of games the Kings won and the number of games the Kings lost in overtime. HOCKEY Write and solve a linear system Hockey team Number of games played Total number of points Los Angeles Kings 82 89 Anaheim Mighty Ducks 82 98

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Write and solve a linear system Example 4 STEP 1Write a system of equations. Let x represent the number of wins, and let y represent the number of games lost in overtime. Equation 1 : Number of games played x ++ = + + = 35y82

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Write and solve a linear system Example 4 STEP 3 Subtract the equations. x 42=– – STEP 2 Rewrite Equation 1 so that the like terms are arranged in columns. x y 47 = 2x y 89 + = x 35 y 82 + = + 2x y 89 = + + Equation 2 : Total number of points 2 + = + = x1y89

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Write and solve a linear system Example 4 STEP 4 Solve for x. x 42= STEP 5 Substitute 42 for x in either equation and solve for y. Write Equation 1. x y 47 =+ Solve for y. y 5 = Substitute 42 for x. 42 y 47 =+ ANSWER The Los Angeles Kings won 42 games and lost 5 games in overtime.

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Guided Practice 5.HOCKEY In Example 4, the Anaheim Mighty Ducks lost 27 games in regulation. How many games did the Ducks win? for Example 4 ANSWER 43 games

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