To get the second equation, use the information that says the Pink Floyd album was on the chart 251 weeks more than the Johnny Mathis album. English: Number of weeks Pink Floyd was on Billboard 200 chart was 251 weeks more than the Johnny Mathis album. T T T T x 251 y The second equation is x 251 y. The system of equations is x y 1231 x 251 y. Step 4: Solve the system. x y 1231 1251 y2 y 1231 Substitute. 251 2y 1231 Combine like terms. 2y 980 Subtract 251 from each side. 2 y 2 980 2 Divide each side by 2. y 490 Simplify. Find x by substituting y 490 into x 251 y. x 251 490 741 The solution to the system is (741, 490). Step 5: Check the answer, and interpret the solution as it relates to the problem. The Dark Side of the Moon was on the Billboard 200 for 741 weeks, and Johnny’s Greatest Hits was on the chart for 490 weeks. They were on the chart for a total of 741 490 1231 weeks, and the Pink Floyd album was on there 741 490 251 weeks longer than the other album. Try using the elimination method to solve this system of linear equations. Next, decide which method is easier for you! YOU TRY 1 Write a system of equations, and solve. In 2010, Carson City, NV, had about 26,100 more citizens than Elmira, NY. Find the population of each city if together they had approximately 84,500 residents. (www.census.gov) Next we will see how we can use two variables and a system of equations to solve geometry problems. www.mhhe.com/messersmith SECTION 4.4 Applications of Systems of Two Equations 275
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