22. −0.4x + 0.25y = −2.175
2x + y = 7.5
6-4 Elimination Using Multiplication
Use elimination to solve each system of
equations.
8. x − y = −8
7x + 5y = 16
ANSWER: (−2, 6)
10. 6x + y = −39
3x + 2y = −15
ANSWER: (−7, 3)
14. 8x + 3y = 4
−7x + 5y = −34
ANSWER: (2, −4)
16. 4x + 7y = −80
3x + 5y = −58
ANSWER: (−6, −8)
20. FOOTBALL A field goal is 3 points and the extra
point after a touchdown is 1 point. In a recent post–
season, Adam Vinatieri of the Indianapolis Colts
made a total of 21 field goals and extra point kicks
for 49 points. Find the number of field goals and
extra points that he made.
ANSWER: (4.5, −1.5)
25. CCSS MODELING A staffing agency for in-home
nurses and support staff places necessary personal at
locations on a daily basis. Each nurse placed works
240 minutes per day at a daily rate of $90. Each
support staff employee works 360 minutes per day at
a daily rate of $120.
a. On a given day, 3000 total minutes are worked by
the nurses and support staff that were placed. Write
an equation that represents this relationship. b. On the same day, $1050 of total wages were
earned by the placed nurses and support staff. Write
an equation that represents this relationship. c. Solve the system of equations, and interpret the
solution in context of the situation.
ANSWER: a. 240n + 360s = 3000 b. 90n + 120s = 1050
c. (5, 5); 5 nurses and 5 support staff employees
were placed.
30. ERROR ANALYSIS Jason and Daniela are
solving a system of equations. Is either of them
correct? Explain your reasoning.
ANSWER: 14 field goals; 7 extra points
Use elimination to solve each system of
equations.
22. −0.4x + 0.25y = −2.175
2x + y = 7.5
ANSWER: (4.5, −1.5)
25. CCSS MODELING A staffing agency for in-home
nurses and support staff places necessary personal at
locations on a daily basis. Each nurse placed works
240 minutes per day at a daily rate of $90. Each
support staff employee works 360 minutes per day at
a daily rate of $120.
a. On a given day, 3000 total minutes are worked by
the nurses and support staff that were placed. Write
an equation that represents this relationship. eSolutions Manual - Powered by Cognero
b. On the same day, $1050 of total wages were
ANSWER: Jason; in order to eliminate the r–terms, you can
multiply the second equation by 2 and then subtract,
or multiply the equation by −2 and then add. Daniela
did not subtract the equations correctly.
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