8.1
10. Solve the system of equations graphically. Then classify the system as consistent or inconsistent and the equations as dependent or independent.
2b+a=11, a-b=5
20. Solve the system of equations graphically. Then classify the system as consistent or inconsistent and the equations as dependent or independent.
A+2b=-3, b-a=6
8.2
12. Solve the system by the substitution method.
4p-2q=16, 5p+7q=1
Divide the first equation by 2:
2p – q = 8
Add q and subtract 8:
Q = 2p-8
Substitute that into the second one:
5p+7(2p-8)=1
5p+14p-56=1
19p = 57
P = 3
Q = 2p-8 = 2(3) – 8 = 6-8 = -2
(3,-2)
16. Solve the system by the substitution method.
4x+13y=5, -6x+ y=13
Add 6x to the second one:
Y=6x+13
Plug that into the first:
4x+13(6x+13)=5
4x+78x+169=5
82x = -164
X = -2
Y = 6(-2) + 13 = -12+13=1
(-2,1)
22. Airplane Seating. An airplane has a total of 152 seats. The number of coach-class seats is 5 more than six times the number of first-class seats. How many of each type of seat are there on the plane?
c+f=152
C=5+6f
Plug the second into the first:
5+6f+f=152
7f+5=152
7f=147
F=21
Get c:
C=5+6(21) = 5+126=131
21 first class, 131 coach
8.3
2. Solve the system by the elimination method
x+y=9, 2x-y =-3
Add the two equations:
3x=6
X = 2
Get y:
2+y=9
Y = 7
(2,7)
16. Solve the system by the elimination method
3x-2y=1, -6x+4y=-2
Multiply the first by 2:
6x-4y=2
Add that to the second:
0=0
That is true, so there are infinite solutions.
32. Use the elimination method when solving the translated system.
Hockey Points. At one time, hockey teams received two points when they won a game and one point when they tied. One season, a team won a championship with 60 points. They won 9 more games than they tied. How many wins and how many ties did the team have?
W=9+t (or w-t=9)
w-t=9
2w+t=60
Add the two equations:
3w=69
W = 23
Get t:
23-t=9
T = 23-9
T = 14
14 ties, 23 wins
8.4
4. Solve
Fundraising. The St. Mark's Community Barbecue served 250 dinners. A child's plate cost $3.50 and an adult's plate cost $7.00. A total of $1347.50 was collected. How many of each type of plate was served?
A+c=250 (total dinners)
3.5c + 7a = 1347.5 (price)
Multiply the first by 3.5:
3.5c+3.5a = 875
Subtract that from the second:
3.5a = 472.5
Divide by 3.5:
A = 135
Use the equation for c:
135+c=250
C = 115
115 children, 135 adults