In Exercises 29–42, solve each system by the method of your choice. $\begin{cases} y = (x + 3)^2 \\ x + 2y = -2 \end{cases}$

Graph the solution set of each system of inequalities or indicate that the system has no solution.

$\begin{cases} x - y \leq 1 \\ x \geq 2 \end{cases}$

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x/4 - y/4 = −1 x + 4y = -9

In Exercises 39–45, graph each inequality. y ≤ (-1/2)x + 2

Graph the solution set of each system of inequalities or indicate that the system has no solution.

$\begin{cases} x + y > 4 \\ x + y < -1 \end{cases}$

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 2x = 3y + 4 4x = 3 - 5y

Write the partial fraction decomposition of each rational expression. (4x²+3x+14)/(x³ - 8)

In Exercises 29–42, solve each system by the method of your choice. $\begin{cases} x^2 + y^2 + 3y = 22 \\ 2x + y = -1 \end{cases}$

In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is 7. If one number is subtracted from the other, their difference is -1. Find the numbers.

Graph the solution set of each system of inequalities or indicate that the system has no solution.

$\begin{cases} x + y > 4 \\ x + y > -1 \end{cases}$

Perform each long division and write the partial fraction decomposition of the remainder term. (x⁵+2)/(x²-1)

In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers. The sum of two numbers is 10 and their product is 24. Find the numbers.

In Exercises 39–45, graph each inequality. y ≤ x^2 - 1

Graph the solution set of each system of inequalities or indicate that the system has no solution.

$\begin{cases} y \geq x^2 - 1 \\ x - y \geq -1 \end{cases}$

Perform each long division and write the partial fraction decomposition of the remainder term. (x⁴-x²+2)/(x³-x²)

In Exercises 39–45, graph each inequality. y ≤ 2^x

In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers. The difference between the squares of two numbers is 3. Twice the square of the first number increased by the square of the second number is 9. Find the numbers.

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.

This

is a piecewise function. Refer to the textbook.

Graph the solution set of each system of inequalities or indicate that the system has no solution.

$\begin{cases} x^2 + y^2 \leq 16 \\ x + y > 2 \end{cases}$

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.

This

is a piecewise function. Refer to the textbook.

In Exercises 47–48, solve each system by the method of your choice. (x + 2)/2 - (y + 4)/3 = 3 (x + y)/5 = (x - y)/2 - 5/2

In Exercises 47–52, solve each system by the method of your choice. $\begin{cases} 2x^2 + xy = 6 \\ x^2 + 2xy = 0 \end{cases}$

In Exercises 47–48, solve each system by the method of your choice. (x - y)/3 = (x + y)/2 - 1/2 (x + 2)/2 - 4 = (y + 4)/3

In Exercises 49–50, solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0, b ≠ 0 5ax + 4y = 17 ax + 7y = 22

In Exercises 47–52, solve each system by the method of your choice. $\begin{cases} -4x + y = 12 \\ y = x^3 + 3x^2 \end{cases}$

Graph the solution set of each system of inequalities or indicate that the system has no solution.

$\begin{cases} x^2 + y^2 > 1 \\ x^2 + y^2 < 16 \end{cases}$

Graph the solution set of each system of inequalities or indicate that the system has no solution.

$\begin{cases} (x - 1)^2 + (y + 1)^2 < 25 \\ (x - 1)^2 + (y + 1)^2 \geq 16 \end{cases}$

Find the partial fraction decomposition for 1/x(x+1) and use the result to find the following sum:

Solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0 and b ≠ 0. For the linear function f(x) = mx + b, f(−2) = 11 and ƒ(3) = -9. Find m and b.

In Exercises 47–52, solve each system by the method of your choice. $\begin{cases} \frac{3}{x^2} + \frac{1}{y^2} = 7 \\ \frac{5}{x^2} - \frac{2}{y^2} = -3 \end{cases}$