Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve each system by graphing or using a table. Check your answers.

7. { y = x − 2 y = − 2 x + 7 left brace . table with 2 rows and 1 column , row1 column 1 , y equals x minus 2 , row2 column 1 , y equals negative 2 x plus 7 , end table
8. { y = − x + 3 y = 3 2 x − 2 left brace . table with 2 rows and 1 column , row1 column 1 , y equals negative x plus 3 , row2 column 1 , y equals , 3 halves , x minus 2 , end table
9. { 2 x + 4 y = 12 x + y = 2 left brace . table with 2 rows and 1 column , row1 column 1 , 2 x plus 4 y equals 12 , row2 column 1 , x plus y equals 2 , end table
10. { x = − 3 y = 5 left brace . table with 2 rows and 1 column , row1 column 1 , x equals negative 3 , row2 column 1 , y equals 5 , end table
11. { 2 x − 2 y = 4 y − x = 6 left brace . table with 2 rows and 1 column , row1 column 1 , 2 x minus 2 y equals 4 , row2 column 1 , y minus x equals 6 , end table
12. { 3 x + y = 5 x − y = 7 left brace . table with 2 rows and 1 column , row1 column 1 , 3 x plus y equals 5 , row2 column 1 , x minus y equals 7 , end table

See Problem 2.

Write and solve a system of equations for each situation. Check your answers.

13. A store sells small notebooks for $8 and large notebooks for $10. If you buy 6 notebooks and spend $56, how many of each size notebook did you buy?
14. A shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50. If you buy 5 bags and spend $17, how many of each size bag did you buy?

See Problem 3.

Graphing Calculator Find linear models for each set of data. In what year will the two quantities be equal?

15. U.S. Life Expectancy at Birth (1970–2000)

    Year	1970	1975	1980	1985	1990	1995	2000
    Men (years)	67.1	68.8	70.0	71.1	71.8	72.5	74.3
    Women (years)	74.7	76.6	77.4	78.2	78.8	78.9	79.7

    SOURCE: U.S. Census Bureau

16. Annual U.S. Consumption of Vegetables

    Year	1980	1985	1990	1995	1998	1999	2000
    Broccoli (lb/person)	1.5	2.6	3.4	4.3	5.1	6.5	6.1
    Cucumbers (lb/person)	3.9	4.4	4.7	5.6	6.5	6.8	6.4

    SOURCE: U.S. Census Bureau

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