91Ó°ÊÓ

Solve each system. \(\left\\{\begin{array}{l}{7 x+2 y=-8} \\ {8 y=4 x}\end{array}\right.\)

For each system, choose the method of solving that seems easier to use. Explain why you made each choice. \(\left\\{\begin{aligned} 3 x-5 y &=26 \\\\-2 x-3 y &=-11 \end{aligned}\right.\)

Economics Resarch shows that in a certain market only 2000 widgets can be sold at \(\$ 8\) each, but if the price is reduced to \(\$ 3,\) then \(10,000\) can be sold. a. Let \(p\) represent price and \(n\) represent the number of widgets. Identify the independent variable and the dependent variable. b. Use the information above to write a linear demand equation. c. A shop can make 2000 widgets for \(\$ 5\) each and \(20,000\) widgets for \(\$ 2\) each. Use this information to write a linear supply equation. d. Find the equilibrium point where supply is equal to demand and profit is a maximum. Explain the meaning of the coordinates of this point within the context of the exercise.

How would you test whether \((2,-2)\) is a solution of the system?

Solve each inequality. Graph the solution on a number line. $$ -4 x+3 \leq 9 $$

A theater production costs \(\$ 40,000\) plus \(\$ 2800\) per performance. A sold- out performance brings in \(\$ 3675 .\) How many sold-out performances will the production need to break even?

Solve each inequality. Graph the solution on a number line. $$ -(x+4)-3 \geq 11 $$

Solve each inequality. Graph the solution on a number line. $$ 2(3 x-1)

Graph each inequality on a coordinate plane. $$ x<-4 $$

Use the following system of equations \(\left\\{\begin{array}{l}{5 x-3 y=11} \\\ {-x+12 y=3.5}\end{array}\right.\) If you want to solve the system by eliminating \(x\) (with addition), by what would you multiply the second equation?