7. Systems of Equations & Matrices

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.

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 price (in dollars).

Solve each problem. The supply and demand equations for a certain commodity are given. supply: p = √(0.1q + 9) - 2 and demand: p = √(25 - 0.1q).

Find the equilibrium demand.

Solve each problem. The supply and demand equations for a certain commodity are given. supply: p = √(0.1q + 9) - 2 and demand: p = √(25 - 0.1q).

Find the equilibrium price (in dollars).

Solve each problem. Find all values of b such that the straight line 3x - y = b touches the circle x² + y² = 25 at only one point.

Solve each problem. Find the equation of the line passing through the points of intersection of the graphs of x² + y² = 20 and x² - y = 0.

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

Solve each problem. See Examples 5 and 9. At the Berger ranch, 6 goats and 5 sheep sell for \$305, while 2 goats and 9 sheep sell for \$285. Find the cost of a single goat and of a single sheep.

Solve each system. (Hint: In Exercises 69–72, let 1/x = t and 1/y = u.)

2/x + 1/y = 3/2

3/x - 1/y = 1

Solve each system by elimination. In systems with fractions, first clear denominators.

2x - 3y = -7

5x + 4y = 17

Solve each system by substitution.

8x - 10y = -22

3x + y = 6

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