91Ó°ÊÓ

For the following exercises, solve each system by substitution. $$ \begin{aligned} x+3 y &=5 \\ 2 x+3 y &=4 \end{aligned} $$

For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth. $$ \begin{aligned} 0.1 x+0.2 y &=0.3 \\\\-0.3 x+0.5 y &=1 \end{aligned} $$

For the following exercises, solve for the desired quantity. A guitar factory has a cost of production \(C(x)=75 x+50,000\) . If the company needs to break even after 150 units sold, at what price should they sell each guitar? Round up to the nearest dollar, and write the revenue function.

For the following exercises, use a system of linear equations with two variables and two equations to solve. Find two numbers whose slim is 28 and difference is 13.

Solve each system by Gaussian elimination. \(\begin{array}{l}{10 x+2 y-14 z=8} \\ {-x-2 y-4 z=-1} \\ {-12 x-6 y+6 z=-12}\end{array}\)

Three numbers sum up to 147. The smallest number is half the munber, which is half the largest number. What are the three numbers?

The top three oil producers in the United States in a certain year are the Gulf of Mexico, Texas, and Alaska. The three regions were responsible for 64% of the United States oil production. The Gulf of Mexico and Texas combined for 47% of oil production. Texas produced 3\(\%\) more than Alaska. What percent of United States oil production came from these regions\(?^{[4]}\)

Explain whether a system of two nonlinear equations can have exactly two solutions. What about exactly three? If not, explain why not. If so, give an example of such a system, in graph form, and explain why your choice gives two or three answers.

When you graph a system of inequalities, will there always be a feasible region? If so, explain why. If not, give an example of a graph of inequalities that does not have a feasible region. Why does it not have a feasible region?

Solve the system of inequalities. Use a calculator to graph the system to confirm the answer. $$\begin{array}{l}{x^{2}+y<3} \\ {y>2 x}\end{array}$$