Chapter 7: Problem 33
Solve the linear syst$$ \begin{aligned} &x+2 y=8\\\ &3 x-2 y=8 \end{aligned} $$em.
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Decide whether the graphs of the two equations are $$ y=4 x+3 ; 2 y-8 x=-3 $$
Describe the graph of a linear system that has the given number of solutions. Sketch an example. exactly one solution
Use the following information. You own a bottle recycling center that receives bottles that are either sorted by color or unsorted. To sort and recycle all of the bottles, you can use up to 4200 hours of human labor and up to 2400 hours of machine time. The system below represents the number of hours your center spends sorting and recycling bottles where \(x\) is the number of tons of unsorted bottles and \(y\) is the number of tons of sorted bottles. \(4 x+y \leq 4200\) \(2 x+y \leq 2400\) \(x \geq 0, y \geq 0\) Graph the system of linear inequalities.
Describe the graph of the system of inequalities. $$\begin{array}{l} 2 x+3 y>-6 \\ 2 x+3 y \geq 6 \end{array}$$
MARBLES In Exercises \(61-63\), consider a bag containing 12 marbles that are either red or blue. A marble is drawn at random. There are three times as many red marbles as there are blue marbles in the bag. Write a linear system to describe this situation.
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