 4.4.1: The ordered pair (3, 2) is a/an of the inequality x + y 7 1 because...
 4.4.2: The set of all points that satisfy a linear inequality in two varia...
 4.4.3: The set of all points on one side of a line is called a/an .
 4.4.4: True or false: The graph of 2x  3y 7 6 includes the line 2x  3y = 6.
 4.4.5: True or false: The graph of the linear equation 2x  3y = 6 is used...
 4.4.6: True or false: When graphing 4x  2y 8, to determine which side of ...
 4.4.7: The solution set of the system e x  y 6 1 2x + 3y 12 is the set of...
 4.4.8: True or false: The graph of the solution set of the system e x  3y...
 4.4.9: x 2 + y 3 6 1
 4.4.10: x 4 + y 2 6 1
 4.4.11: y 7 1 3 x
 4.4.12: y 7 1 4 x
 4.4.13: y 3x + 2
 4.4.14: y 2x  1
 4.4.15: y 6  1 4 x
 4.4.16: y 6  1 3 x
 4.4.17: x 2
 4.4.18: x 4
 4.4.19: y 7 4
 4.4.20: y 7 2
 4.4.21: y 0
 4.4.22: x 0
 4.4.23: e 3x + 6y 6 2x + y 8
 4.4.24: e x  y 4 x + y 6
 4.4.25: e 2x  5y 10 3x  2y 7 6
 4.4.26: e 2x  y 4 3x + 2y 7 6
 4.4.27: e y 7 2x  3 y 6 x + 6
 4.4.28: e y 6 2x + 4 y 6 x  4
 4.4.29: e x + 2y 4 y x  3
 4.4.30: e x + y 4 y 2x  4
 4.4.31: e x 2 y 1
 4.4.32: e x 3 y 1
 4.4.33: 2 x 6 5
 4.4.34: 2 6 y 5
 4.4.35: e x  y 1 x 2
 4.4.36: e 4x  5y 20 x 3
 4.4.37: e x + y 7 4 x + y 6 1
 4.4.38: e x + y 7 3 x + y 6 2
 4.4.39: e x + y 7 4 x + y 7 1
 4.4.40: e x + y 7 3 x + y 7 2
 4.4.41: x  y 2 x 2 y 3
 4.4.42: 3x + y 6 x 2 y 4
 4.4.43: x 0 y 0 2x + 5y 10 3x + 4y 12
 4.4.44: x 0 y 0 2x + y 4 2x  3y 6
 4.4.45: 3x + y 6 2x  y 1 x 2 y 4
 4.4.46: 2x + y 6 x + y 2 1 x 2 y 3
 4.4.47: The yvariable is at least 4 more than the product of 2 and the x...
 4.4.48: The yvariable is at least 2 more than the product of 3 and the x...
 4.4.49: The sum of the xvariable and the yvariable is at most 4. The yva...
 4.4.50: The sum of the xvariable and the yvariable is at most 3. The yva...
 4.4.51: x 2 y 3
 4.4.52: x 1 y 2
 4.4.53: Graph the union of y 7 3 2 x  2 and y 6 4.
 4.4.54: Graph the union of x  y 1 and 5x  2y 10.
 4.4.55: 3x + y 6 9 3x + y 7 9
 4.4.56: 6x  y 24 6x  y 7 24
 4.4.57: 3x + y 9 3x + y 9
 4.4.58: 6x  y 24 6x  y 24
 4.4.59: a. What are the coordinates of point A and what does this mean in t...
 4.4.60: a. What are the coordinates of point B and what does this mean in t...
 4.4.61: Write a system of inequalities that models the target heart rate ra...
 4.4.62: Write a system of inequalities that models the target heart rate ra...
 4.4.63: On your next vacation, you will divide lodging between large resort...
 4.4.64: a. An elevator can hold no more than 2000 pounds. If children avera...
 4.4.65: What is a linear inequality in two variables? Provide an example wi...
 4.4.66: How do you determine if an ordered pair is a solution of an inequal...
 4.4.67: What is a halfplane?
 4.4.68: What does a solid line mean in the graph of an inequality?
 4.4.69: What does a dashed line mean in the graph of an inequality?
 4.4.70: Explain how to graph x  2y 6 4.
 4.4.71: What is a system of linear inequalities?
 4.4.72: What is a solution of a system of linear inequalities?
 4.4.73: Explain how to graph the solution set of a system of inequalities.
 4.4.74: What does it mean if a system of linear inequalities has no solution?
 4.4.75: y 4x + 4
 4.4.76: y 2 3 x  2
 4.4.77: 2x + y 6
 4.4.78: 3x  2y 6
 4.4.79: Does your graphing utility have any limitations in terms of graphin...
 4.4.80: Use a graphing utility with a SHADE feature to verify any five of t...
 4.4.81: Use a graphing utility with a SHADE feature to verify any five of t...
 4.4.82: When graphing a linear inequality, I should always use (0, 0) as a ...
 4.4.83: If you want me to graph x 6 3, you need to tell me whether to use a...
 4.4.84: When graphing 3x  4y 6 12, its not necessary for me to graph the l...
 4.4.85: Linear inequalities can model situations in which Im interested in ...
 4.4.86: The graph of 3x  5y 6 10 consists of a dashed line and a shaded ha...
 4.4.87: The graph of y x + 1 consists of a solid line that rises from left...
 4.4.88: The ordered pair (2, 40) satisfies the following system: e y 9x + ...
 4.4.89: For the graph of y 6 x  3, the points (0, 3) and (8, 5) lie on th...
 4.4.90: Write a linear inequality in two variables whose graph is shown.
 4.4.91: In Exercises 9192, write a system of inequalities for each graph.
 4.4.92: In Exercises 9192, write a system of inequalities for each graph.
 4.4.93: Write a linear inequality in two variables satisfying the following...
 4.4.94: Write a system of inequalities whose solution set includes every po...
 4.4.95: Sketch the graph of the solution set for the following system of in...
 4.4.96: Solve using matrices: e 3x  y = 8 x  5y = 2. (Section 3.4, Examp...
 4.4.97: Solve by graphing: e y = 3x  2 y = 2x + 8. (Section 3.1, Example 2)
 4.4.98: Evaluate: 3 8 2 1 3 0 5 6 3 4 3 . (Section 3.5, Example 3)
 4.4.99: a. Graph the solution set of the system: x + y 6 x 8 y 5. b. List t...
 4.4.100: a. Graph the solution set of the system: x 0 y 0 3x  2y 6 y x + 7...
 4.4.101: Bottled water and medical supplies are to be shipped to survivors o...
Solutions for Chapter 4.4: Linear Inequalities in Two Variables
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 4.4: Linear Inequalities in Two Variables
Get Full SolutionsChapter 4.4: Linear Inequalities in Two Variables includes 101 full stepbystep solutions. Since 101 problems in chapter 4.4: Linear Inequalities in Two Variables have been answered, more than 29807 students have viewed full stepbystep solutions from this chapter. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

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).

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

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!).

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Solvable system Ax = b.
The right side b is in the column space of A.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.