91Ó°ÊÓ

Write the linear system whose solution set is {(6, 2)}. Express each equation in the system in slope-intercept form.

Write the linear system whose solution set is \(\varnothing .\) Express each equation in the system in slope-intercept form.

A planet's orbit follows a path described by \(16 x^{2}+4 y^{2}=64\). A comet follows the parabolic path \(y=x^{2}-4 .\) Where might the comet intersect the orbiting planet?

Graph the solution set of each system of inequalities or indicate that the system has no solution. $$ \left\\{\begin{array}{l} {3 x+y \leq 6} \\ {x>-2} \\ {y \leq 4} \end{array}\right. $$

A company that manufactures bicycles has a fixed cost of \(\$ 100,000 .\) It costs \(\$ 100\) to produce each bicycle. The selling price is \(\$ 300\) per bike. (In solving this exercise, let \(x\) represent the number of bicycles produced and sold.)

Write each sentence as an inequality in twovariables. Then graph the inequality. The y-variable is at least 4 more than the product of -2 andthe x-variable.

Rewrite each inequality in the system without absolute value bars. Then graph the rewritten system in rectangular coordinates. $$ \left\\{\begin{array}{l} {|x| \leq 2} \\ {|y| \leq 3} \end{array}\right. $$

How many ounces of a 15% alcohol solution must be mixed with 4 ounces of a 20% alcohol solution to make a 17% alcohol solution?

When a crew rows with the current, it travels 16 miles in 2 hours. Against the current, the crew rows 8 miles in 2 hours. Let \(x=\) the crew's rowing rate in still water and let \(y=\) the rate of the current. The following chart summarizes this information: