 33.1: x 4 2. y 4x  3 y > 2 y
 33.2: y 4x  3 y > 2 y > 4x + 1
 33.3: x  1 2 4. y 3x + 3 x + y > 2 y
 33.4: y 3x + 3 x + y > 2 y < 3x  2
 33.5: Graph the region that shows how many packages of each item he can p...
 33.6: Give an example of three different purchases he can make.
 33.7: y x 8. y x 3 y 3 y x + 7 3y + 5x 16
 33.8: y x 3 y 3 y x + 7 3y + 5x 16 x + y 11 x + y 1
 33.9: x 2 10. x 1 11. y < 2 x y > 3
 33.10: x 1 11. y < 2 x y > 3 y 4
 33.11: y < 2 x y > 3 y 4 y > x + 4
 33.12: x > 1 x 1
 33.13: 3x + 2y 6 14. 4x 3y < 7 x 1 4x y 2
 33.14: 4x 3y < 7 x 1 4x y 2 2y x < 6
 33.15: 3y 2x 8 16. y > x 3 17. 2x + 5y 15 y _2 3 x 1
 33.16: y > x 3 y 2
 33.17: 2x + 5y 15 y _2 3 x 1 y 2 y > _ 2 5 x + 2
 33.18: PARTTIME JOBS Rondell makes $10 an hour cutting grass and $12 an h...
 33.19: RECORDING Janes band wants to spend no more than $575 recording the...
 33.20: y 0 2 x + 2y 8
 33.21: y 4 x 0 y 2x + 2
 33.22: x 3 23. x + y 9 x + 3y 12 x 2y 12 4x +3y 12
 33.23: x + y 9 x + 3y 12 x 2y 12 4x +3y 12 y 2x + 3
 33.24: GEOMETRY Find the area of the region defined by the system of inequ...
 33.25: GEOMETRY Find the area of the region defined by the system of inequ...
 33.26: Write and graph the system of inequalities that represents the rang...
 33.27: On August 29, 2005, Hurricane Katrina hit the Gulf coasts of Louisi...
 33.28: Graph the inequalities that represent how many loaves of each type ...
 33.29: List three different combinations of breads they can make.
 33.30: Which combination uses all of the available flour and baking soda?
 33.31: y < 2x  3 32. x 3 33. x + 1 3 y _1 2 x + 1
 33.32: x 3 33. x + 1 3 y _1 2 x + 1 y > 1
 33.33: x + 1 3 y _1 2 x + 1 y > 1 x + 3y 6
 33.34: y 2x + 1 35. x  3y > 2 36. x 1 y 2x  2 2x  y < 4 y < 2x + 1 3x +...
 33.35: x  3y > 2 36. x 1 y 2x  2 2x  y < 4 y < 2x + 1 3x + y 9 2x + 4y 7
 33.36: x 1 y 2x  2 2x  y < 4 y < 2x + 1 3x + y 9 2x + 4y 7 x + 2y 3
 33.37: OPEN ENDED Write a system of inequalities that has no solution.
 33.38: REASONING Determine whether the following statement is true or fals...
 33.39: CHALLENGE Find the area of the region defined by x + y 5 and x + y 2
 33.40: Writing in Math Using the information about blood pressure on page ...
 33.41: ACT/SAT Choose the system of inequalities whose solution is represe...
 33.42: REVIEW To be a member of the marching band, a student must have a G...
 33.43: 4x  y = 20
 33.44: 3x  4y = 2
 33.45: 3x  4y = 2 45. 4x + 5y = 7 x + 2y = 13 5x + 2y = 40
 33.46: y = 2x + 1 47. 2x + y = 3 48. 2x  y = 6 y = _1 2 x  4
 33.47: 2x + y = 3 48. 2x  y = 6 y = _1 2 x  4 6x + 3y = 9
 33.48: 2x  y = 6 y = _1 2 x  4 6x + 3y = 9 x + 8y = 12
 33.49: RENTALS To rent an inflatable trampoline for parties, it costs $75 ...
 33.50: f(2)
 33.51: g(1)
 33.52: g(3)
 33.53: g(0.25)
Solutions for Chapter 33: Solving Systems of Inequalities by Graphing
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 33: Solving Systems of Inequalities by Graphing
Get Full SolutionsChapter 33: Solving Systems of Inequalities by Graphing includes 53 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Since 53 problems in chapter 33: Solving Systems of Inequalities by Graphing have been answered, more than 59294 students have viewed full stepbystep solutions from this chapter. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. This expansive textbook survival guide covers the following chapters and their solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Column space C (A) =
space of all combinations of the columns of A.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).