 8.7.1: Solve the inequality: 3x + 4 6 8  x
 8.7.2: Graph the equation: 3x  2y = 6
 8.7.3: Graph the equation: x2 + y2 = 9
 8.7.4: Graph the equation: y = x2 + 4
 8.7.5: True or False The lines and are parallel.
 8.7.6: The graph of may be obtained by shifting the graph of _____ to the ...
 8.7.7: When graphing an inequality in two variables, if the inequality is ...
 8.7.8: The graph of the corresponding equation of a linear inequality is a...
 8.7.9: True or False The graph of a system of inequalities must have an ov...
 8.7.10: If a graph of a system of linear inequalities cannot be contained i...
 8.7.11: x 0
 8.7.12: y 0
 8.7.13: x 4
 8.7.14: y 2
 8.7.15: 2x + y 6
 8.7.16: 3x + 2y 6
 8.7.17: x2 + y2 7 1
 8.7.18: x2 + y2 9
 8.7.19: y x2  1
 8.7.20: y 7 x2 + 2
 8.7.21: xy 4
 8.7.22: xy 1
 8.7.23: b x + y 2 2x + y 4
 8.7.24: b 3x  y 6 x + 2y 2
 8.7.25: b 2x  y 4 3x + 2y 6
 8.7.26: b 4x  5y 0 2x  y 2
 8.7.27: b 2x  3y 0 3x + 2y 6
 8.7.28: b 4x  y 2 x + 2y 2
 8.7.29: b x  2y 6 2x  4y 0
 8.7.30: b x + 4y 8 x + 4y 4
 8.7.31: b 2x + y 2 2x + y 2
 8.7.32: b x  4y 4 x  4y 0
 8.7.33: b 2x + 3y 6 2x + 3y 0
 8.7.34: b 2x + y 0 2x + y 2
 8.7.35: b x2 + y2 9 x + y 3
 8.7.36: e x2 + y2 9 x + y 3
 8.7.37: b y x2  4 y x  2
 8.7.38: b y2 x y x
 8.7.39: b x2 + y2 16 y x2  4
 8.7.40: b x2 + y2 25 y x2  5
 8.7.41: b xy 4 y x2 + 1
 8.7.42: b y + x2 1 y x2  1
 8.7.43: d x 0 y 0 2x + y 6 x + 2y 6
 8.7.44: d x 0 y 0 x + y 4 2x + 3y 6
 8.7.45: d x 0 y 0 x + y 2 2x + y 4
 8.7.46: d x 0 y 0 3x + y 6 2x + y 2
 8.7.47: e x 0 y 0 x + y 2 2x + 3y 12 3x + y 12
 8.7.48: e x 0 y 0 x + y 2 x + y 8 2x + y 10
 8.7.49: e x 0 y 0 x + y 2 x + y 8 2x + y 10
 8.7.50: e x 0 y 0 x + y 2 x + y 8 x + 2y 1
 8.7.51: d x 0 y 0 x + 2y 1 x + 2y 10
 8.7.52: f x 0 y 0 x + 2y 1 x + 2y 10 x + y 2 x + y 8
 8.7.53: y 2 8 2 (4, 2) 8 (0, 6) (0, 0) (4, 0) x
 8.7.54: y 2 8 2 (4, 2) 8 (0, 6) (0, 0) (4, 0) x
 8.7.55: y 40 20 (20, 30) (20, 20) (0, 15) (0, 50) (15, 15) 10 30 50
 8.7.56: 10 5 2 (5, 6) (5, 2) (4, 0) (0, 3) (0, 6)
 8.7.57: Financial Planning A retired couple has up to $50,000 to invest. As...
 8.7.58: Manufacturing Trucks Mikes Toy Truck Company manufactures two model...
 8.7.59: Blending Coffee Bills Coffee House, a store that specializes in cof...
 8.7.60: Mixed Nuts Nolas Nuts, a store that specializes in selling nuts, ha...
 8.7.61: Transporting Goods A small truck can carry no more than 1600 pounds...
Solutions for Chapter 8.7: Systems of Inequalities
Full solutions for College Algebra  9th Edition
ISBN: 9780321716811
Solutions for Chapter 8.7: Systems of Inequalities
Get Full SolutionsChapter 8.7: Systems of Inequalities includes 61 full stepbystep solutions. College Algebra was written by and is associated to the ISBN: 9780321716811. Since 61 problems in chapter 8.7: Systems of Inequalities have been answered, more than 32900 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 9.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

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].

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Outer product uv T
= column times row = rank one matrix.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.