Download 15. 3x + 5y = º16 x + 5y = 8 5x º 4y = 26 º2x + 6y = º36 17. 2 º 7x = 9y

Use the substitution method to solve the linear system.
7. x + 3y = 9
4x º 2y = º6
7.3
8. º2x º 5y = 7
9. 4x º 3y = º2
7x + y = º8
10. ºx + 3y = 24
11. 4x + 9y = 2
5x + 8y = º5
2x + 6y = 1
4x + y = 4
12. 9x + 6y = 3
3x º 7y = º26
Examples on
pp. 411–413
SOLVING LINEAR SYSTEMS BY LINEAR COMBINATIONS
To solve the linear system,
2x º 15y = º10
get coefficients for x or y that are opposites.
º4x + 5y = º30
4x º 30y = º20
Multiply Equation 1 by 2.
º4x + 5y = º30
Write Equation 2.
º25y = º50
Add the equations.
y= 2
Solve for y.
EXAMPLE
Equation 1
Equation 2
Then substitute 2 for y in Equation 2 and solve for x.
º4x + 5y = º30
Write Equation 2.
º4x + 5(2) = º30
x = 10
Substitute 2 for y.
Solve for x.
The solution is (10, 2). Check the solution in the original equations.
Use linear combinations to solve the linear system.
13. º4x º 5y = 7
x + 5y = 8
16. 9x + 6y = 3
3y + 6x = 18
7.4
14. 2x + y = 0
5x º 4y = 26
17. 2 º 7x = 9y
2y º 4x = 6
15. 3x + 5y = º16
º2x + 6y = º36
18. 4x º 9y = 1
º5x + 6y = 4
Examples on
pp. 418–420
APPLICATIONS OF LINEAR SYSTEMS
EXAMPLES After you model a real-life problem with a linear system, you have a
choice of three methods for solving the system.
GRAPHING: Use to approximate a solution.
SUBSTITUTION: Use when one variable has a coefficient of 1 or º1.
LINEAR COMBINATIONS: Use when no variable has a coefficient of 1 or º1.
19.
20.
CARNIVAL You have 50 tickets to ride the Ferris wheel and the roller
coaster. If you ride 12 times, using 3 tickets for each Ferris wheel ride and 5
tickets for each roller coaster ride, how many times did you go on each ride?
RENTING MOVIES You spend $13 to rent five movies for the weekend.
Since new releases rent for $3 and regular movies rent for $2, how many
regular movies did you rent? How many new releases did you rent?
33A
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