Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.

2xy + 1 = 0

x + 16y = 2

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.

3x² - y² = 11

xy = 12

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose ratio is 9 to 2 and whose product is 162.

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose ratio is 4 to 3 and are such that the sum of their squares is 100.

Answer each question. Does the straight line 3x - 2y = 9 intersect the circle x² + y² = 25? (Hint: To find out, solve the system formed by these two equations.)

Answer each question. A line passes through the points of intersection of the graphs of y = x² and x² + y² = 90. What is the equation of this line?

Solve each problem. Find the radius and height (to the nearest thousandth) of an open-ended cylinder with volume 50 in.³ and lateral surface area 65 in.².

Solve each problem. The supply and demand equations for a certain commodity are given. supply: p = 2000/(2000 - q) and demand: p = (7000 - 3q)/2q.

Find the equilibrium demand.