Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7.

4x + 3y = -7

2x + 3y = -11

Graph the solution set of each system of inequalities.

$e^{x}-y\le1$

$x-2y\ge4$

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7.

$5x+4y=10$

$5x+4y=10$

Find each product, if possible.

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.

Given and $C = \left[ \begin{matrix} -5 & 4 & 1 \\ 0 & 3 & 6 \end{matrix} \right]$, find each product, if possible. See Examples 5–7. BA

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. 1.5

x + 3y = 5

2x + 4y = 3

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 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).

Find the values of the variables for which each statement is true, if possible.

Given , and $C = \left[ \begin{matrix} -5 & 4 & 1 \\ 0 & 3 & 6 \end{matrix} \right]$, find each product, if possible. See Examples 5–7. BC

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

$\frac{2}{x}+\frac{3}{y}=18$

$\frac{4}{x}-\frac{5}{y}=-8$

Perform each operation, if possible.

$\left[\begin{array}{c}3\\ 2\\ 5\end{array}\right]-\left[\begin{array}{c}8\\ -4\\ 6\end{array}\right]+\left[\begin{array}{c}1\\ 0\\ 2\end{array}\right]$

Given , and $C = \left[ \begin{matrix} -5 & 4 & 1 \\ 0 & 3 & 6 \end{matrix} \right]$, find each product, if possible. See Examples 5–7. AB

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7.

(1/2)x + (1/3)y = 2

(3/2)x - (1/2)y = -12

Consider the following nonlinear system. Work Exercises 75 –80 in order.

y = | x - 1 |

y = x² - 4

How is the graph of y = | x - 1 | obtained by transforming the graph of y = | x |?

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7.

2x - y + 4z = -2

3x + 2y - z = -3

x + 4y - 2z = 17

For what value(s) of k will the following system of linear equations have no solution? infinitely many solutions?

x - 2y = 3

-2x + 4y = k

Perform each operation, if possible.

Consider the following nonlinear system. Work Exercises 75 –80 in order.

y = | x - 1 |

y = x² - 4

Use the definition of absolute value to write y = | x - 1 | as a piecewise-defined function.

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7.

x + 2y + 3z = 4

4x + 3y + 2z = 1

-x - 2y - 3z = 0

Use a system of equations to solve each problem. See Example 8. Find an equation of the line y = ax + b that passes through the points (-2, 1) and (-1, -2).

Perform each operation, if possible.

The graphs show regions of feasible solutions. Find the maximum and minimum values of each objective function. objective function = 3x + 5y

Perform each operation, if possible.

Find the maximum and minimum values of each objective function over the region of feasible solutions shown at the right. objective function = 3x + 5y