Meadows Review (Entire Unit including last semester portion)
Name___________________________________
Write the equation of the line in point-slope, slope intercept and standard forms.
4
3
2
5
and - , 1) - , 9
4
9
8
Decide whether the pair of lines is parallel, perpendicular, or neither.
2) 12x + 4y = 16 and 9x + 3y = 15
Solve the system of inequalities. (In other words, find the feasible region if it exists.)
3) 3x + 3y 18
2x + 4y 24
x+y 2
x 0
y 0
Solve the problem.
4) Find the minimum value of f = 2x + 4y subject to the following constraints.
x + 2y 10
3x + y 10
x 0
y 0
1)
2)
3)
4)
Solve the system. If the system is inconsistent or has dependent equations, say so.
5) 5x - 2y = -1
x + 4y = 35
5)
Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.
6) x - 4y = -4
-4x - 3y = -3
6)
HONORS ONLY: Solve by any method. Assume a and b represent nonzero constants.
7) ax + by = 2
2ax + 4by = 1
7)
1
Solve the system of equations.
8) 7x + 7y + z = 1
x + 8y + 8z = 8
9x + y + 9z = 9
8)
Solve the system of equations . If the system is inconsistent or has dependent equations, say so.
9)
x - y + 4z = 24
-2x + 2y - 8z = 5
x + 4y + z = 21
10)
x + 4y - z = 3
-4x - 16y + 4z = -12
3x + 12y - 3z = 9
9)
10)
Solve the system by hand. Express the solution in the form (x, y, z, w).
11)
5x - 5z + w = -10
-x + 5y + z - 5w = 6
2x - y + 5w = -17
y - 5z - w = -14
11)
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
12) (-1.2, -3.3) and (0.8, 1.1)
12)
Decide whether the pair of lines is parallel, perpendicular, or neither.
13) 3x - 8y = 16 and 32x + 12y = 5
13)
14) The line through (-20, 5) and (-4, 7) and the line through (-5, 5) and (7, 4)
14)
15) y + 11 = -4x and 5y = 10x - 16
15)
Write the equation in slope-intercept form.
16) 3x - 10y = -6
16)
17) -x + 6y = 3
17)
Find an equation of the line passing through the two points. Write the equation in standard form.
18) (10, 9) and (10, 1)
2
18)
Graph the linear inequality in two variables.
19) x + 2y -5
19)
20) y < -4
20)
21) 3x + 5y 15
21)
Solve the problem.
22) A woman made a deposit of $181. If her deposit consisted of 61 bills, some of them
one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she
deposit?
Solve the problem by using three variables.
23) The sum of the ages of Art, Ben, and Cal is 59. Art is 1 year older than Cal and Cal is 1 year
younger than Ben. Who, if anyone, was a teenager 7 years ago?
3
22)
23)
24) A basketball fieldhouse seats 15,000. Courtside seats sell for $8, endzone for $6, and
balcony for $5. The total revenue from a sell-out is $86,000. If half the courtside and
balcony seats and all the endzone seats are sold, the total revenue is $49,000. How many of
each type are there?
Use matrices to solve the system.
25) -5x - y - 7z = -40
-3x + 7y + 4z = 62
6x - 8y + z = -46
24)
25)
Provide an appropriate response.
26) Give the dimensions of the following matrix.
1 2 3
-6 -5 -4
2 -1 2
4 -7 0
26)
Find the indicated matrix.
27) Let A = -3 3 . Find 3A.
02
27)
28) Let A = [-4 2] and B = [1 0]. Find 2A + 3B.
28)
Find the indicated matrix product or state that the product is undefined.
0 1 0
2 4 -2
29) A = 0 0 1 , B = -2 -8 1
1 0 0
-6 2 -7
29)
BA
Determine whether the matrices are inverses.
1 1
2 4
30) -2 4 , 1 1
4 -4
2 4
31)
6 -5
-3 5
,
30)
1 1
3 3
31)
1 2
5 5
Find the inverse of A if it has one, or state that the inverse does not exist.
32) A = -3 0
-4 5
4
32)
Solve the system of equations.
33) x + 2y - 3z + w = 7
33)
3x + 4y - z + 2w = 4
-2x + y + z - w = -3
x - y + 2z - 2w = 1
34) 3x + 5y
- 2w = -13
34)
2x + 7z - w = -1
4y + 3z + 3w = 1
-x + 2y + 4z
= -5
Solve the problem.
35) Find the maximum value of f = 8x + 12y subject to the following constraints.
40x + 80y 560
6x + 8y 72
x 0
y 0
36) An airline with two types of airplanes, P1 and P2 , has contracted with a tour group to
provide transportation for a minimum of 400 first class, 750 tourist class, and 1500
economy class passengers. For a certain trip, airplane P1 costs $10,000 to operate and can
accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane P2
costs $8500 to operate and can accommodate 18 first class, 30 tourist class, and 44 economy
class passengers. How many of each type of airplane should be used in order to minimize
the operating cost?
5
35)
36)