Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary.

2x + 6y = 6

5x + 9y = 9

How many rows and how many columns does this matrix have? What is its dimension?

Match each system of inequalities with the correct graph from choices A–D. x ≥ 5 y ≤ -3

Fill in the blank(s) to correctly complete each sentence. For the following statement to be true, the value of x must be ____, and the value of y must be ____.

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. The following nonlinear system has two solutions, one of which is (3,____).

x + y = 7

x² + y² = 25

Answer each question. What is the product of and I₂ (in either order)?

Answer each question. By what expression should we multiply each side of 5/((3x(2x + 1)) = A/(3x) + B/(2x + 1) so that there are no fractions in the equation?

What is the value of ?

Answer each question. What is the product ?

What is the augmented matrix of the following system?

-3x + 5y = 2

6x + 2y = 7

Answer each question. By what expression should we multiply each side of (3x - 2)/(x + 4)(3x^2 + 1) = A/(x + 4) + (Bx + C)/(3x^2 + 1) so that there are no fractions in the equation?

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. The following nonlinear system has two solutions, one of which is (___, 3).

2x + y = 1

x² + y² = 10

What expression in x represents ?

Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary.

$\frac{1}{6x}+\frac{1}{3y}=8$

$\frac{1}{4x}+\frac{1}{2y}=12$

What is the value of x if ?

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. If we want to solve the following nonlinear system by substitution and we decide to solve equation (2) for y, what will be the resulting equation when the substitution is made into equation (1)?

x² + y = 2 (1)

x - y = 0 (2)

If the dimension of matrix A is 3 $\times$ 2 and the dimension of matrix B is 2 $\times$ 6, then the dimension of AB is ____.

Answer each question. By what expression should we multiply each side of (3x - 1)/(x(2x^2 + 1)^2) = A/x + (Bx + C)/(2x^2 + 1) + (Dx + E)/(2x^2 + 1)^2 so that there are no fractions in the equation?

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 5/(3x(2x + 1))

Solve each system by substitution.

4x + 3y = -13

-x + y = 5

Evaluate each determinant.

Find the dimension of each matrix. Identify any square, column, or row matrices.

Use the given row transformation to change each matrix as indicated.

Find the dimension of each matrix. Identify any square, column, or row matrices.

Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary.

6x + 10y = -11

9x + 6y = -3

Verify that the points of intersection specified on the graph of each nonlinear system are solutions of the system by substituting directly into both equations.

2x² = 3y + 23

y = 2x - 5

Use the given row transformation to change each matrix as indicated.

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I_n.)

Use the given row transformation to change each matrix as indicated.

Find the dimension of each matrix. Identify any square, column, or row matrices.