Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.

$5x^2-2y^2=25$

$10x^2+y^2=50$

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. The longest side of a right triangle is 13 m in length. One of the other sides is 7 m longer than the shortest side. Find the lengths of the two shorter sides of the triangle.

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.