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103
106 1 140 1
Problem
103
106 4 140
103
106 10 140
Problem
Verify that (2, 3) is a solution to
Solve the system by graphing.
x
0
y
-2
2
0
x
y
0
6
6
0
The solution is (4, 2)
Bitt13.1-1
Bitt13.1-11
Blit8.1-3
Blit8.1-x
1
103
106 8 140 3
Problem
Solve:
Problem
x + 3y = 8
Solve:
y = 2x  9
x + 3(2x  9) = 8
y = 2(5)  9
x + 6x  27 = 8
y = 10  9
7x = 35
y=1
x=5
The solution to the system of equations is (5, 1).
Bitt13.2-1
Blit8.1-7
The solution to the system of equations is
Bitt13.2-11
Blit8.1-13
.
103
106 12 140
Problem
103
106 16 140 7
103
106 18 140 9
Problem
The perimeter of a basketball court is 288 ft and the
length is 44 ft longer than the width. Find the
dimensions of the court.
Solve:
4x + 3y = 15
2x  5y = 1
Eliminate x.
4x + 3y = 15
2x  5(1) = 1
 4x + 10y =  2
2x  5 = 1
13y = 13
2x = 6
y=1
x=3
The solution is (3, 1).
The court is 50 ft wide and 94 ft long.
Bitt13.2-19
Bitt13.3-15
Blit8.1-77
Blit8.1-25
2
103
106 15 140 12
Problem
Solve the system
3y = 2x  4
Problem
Solve the system
6y = 4x  3
 6y =  4x + 8
6y =
4x  3
0=5
There are no values of x and y for which 0 = 5. So
this system has no solution. The graphs of the
equations are of parallel lines.
Bitt13.3-11
Blit8.1-41mml
y = 3x  5
21x  35 = 7y
 21x + 35 = 7y
21x  35 = 7y
0=0
The equation 0 = 0 indicates that the equations are
dependent. There are infinitely many solutions.
The graphs of the equations are identical.
Bitt13.3-29
Blit8.1-33
103
106 19 140
103
106 22 140
Problem
Problem
In one game, the Spurs scored 85 points on a
combination of 39 two- and three-point baskets.
How many of each type shot were made?
How many liters of 50% acid and 80% acid must be
mixed to make 100 L of a 68% acid solution?
2-pt
3-pt
Total
shots
x
y
39
points
2x
3y
85
50% 80%
quantity
acid
The Spurs made 32 two-point shots and 7 threepoint shots.
Bitt13.4-1
68%
x
y
100
0.5x
0.8y
0.68(100)
40 L of 50% acid and 60 L of 80% acid are required
to make 100 L of 68% acid.
Bitt13.4-13
Blit8.1-77
3
Blit8.1-79