Graph the solution set of each system of inequalities.

$x\le4$

$x\ge0$

$y\ge0$

$x+2y\ge2$

Graph the solution set of each system of inequalities.

$2y+x\ge-5$

$y\le3+x$

$x\le0$

$y\le0$

Graph the solution set of each system of inequalities.

$2x+3y\le12$

$2x+3y>-6$

$3x+y\lt{4}$

$x\ge0$

$y\ge0$

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.

Use the determinant theorems to evaluate each determinant. See Example 4.

Graph the solution set of each system of inequalities.

$y\le x^3-x$

$y>-3$

Graph the solution set of each system of inequalities.

$y\ge3^{x}$

$y\ge2$

Graph the solution set of each system of inequalities.

$y\le\log x$

$y\ge\left|x-2\right|$

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.

$5x+4y=10$

$5x+4y=10$

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.

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

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

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

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

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