In Exercises 29–42, solve each system by the method of your choice. $\begin{cases} 2x^2 + y^2 = 18 \\ xy = 4 \end{cases}$

In Exercises 29–42, solve each system by the method of your choice. $\begin{cases} x^2 + 4y^2 = 20 \\ x + 2y = 6 \end{cases}$

In Exercises 29–42, solve each system by the method of your choice. $\begin{cases} x^3 + y = 0 \\ x^2 - y = 0 \end{cases}$

In Exercises 29–42, solve each system by the method of your choice. $\begin{cases} x^2 + (y - 2)^2 = 4 \\ x^2 - 2y = 0 \end{cases}$

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

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

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

Find the length and width of a rectangle whose perimeter is 36 feet and whose area is 77 square feet.

Find the length and width of a rectangle whose perimeter is 40 feet and whose area is 96 square feet.

Ggraph each inequality. x+2y≤8

Graph each inequality. x−2y>10

Graph each inequality. y≤(1/3)x

Graph each inequality. y>2x−1

Graph each inequality. x≤−3

Graph each inequality. y>−3

Graph each inequality. x²+y²≤1

Graph each inequality. (x−2)²+(y+1)²<9

Graph each inequality. y < x² - 1

Graph each inequality. y≥x²−9

Graph each inequality. y>2^x

Graph each inequality. y≥log₂(x+1)

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

$\begin{cases} 3x + 6y \leq 6 \\ 2x + y \leq 8 \end{cases}$

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

$\begin{cases} 2x - 5y \leq 10 \\ 3x - 2y > 6 \end{cases}$

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

$\begin{cases} y > 2x - 3 \\ y < -x + 6 \end{cases}$

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

$\begin{cases} x + 2y \leq 4 \\ y \geq x - 3 \end{cases}$

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

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