Chapter 7: Problem 41
Use substitution to I solve the linear system. Then use a graphing calculator or a computer to check your solution. $$\begin{aligned} &1.5 x-y=40.0\\\ &0.5 x+0.5 y=10.0 \end{aligned}$$
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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. \(4 x+y \leq 4200\) \(2 x+y \leq 2400\) \(x \geq 0, y \geq 0\) a. Find the vertices of your graph. b. You will earn 30 dollar per ton for bottles that are sorted by color and earn 10 dollar per ton for unsorted bottles. Let \(P\) be the maximum profit. Substitute the ordered pairs from part (a) into the following equation and solve. $$ P=10 x+30 y $$ c. Assuming that the maximum profit occurs at one of the four vertices, what is the maximum profit?
Use substitution to solve the linear system. $$\begin{aligned} &d-e=8\\\ &\frac{1}{5} d=e+4 \end{aligned}$$
Describe the graph of a linear system that has the given number of solutions. Sketch an example. no solution
Use the substitution method or linear combinations to solve the linear system and tell how many solutions the system has. $$ \begin{aligned}&-4 x+y=-8\\\&-12 x+3 y=-24\end{aligned} $$
Use substitution to solve the linear system. $$\begin{aligned} &\frac{3}{5} b-a=0\\\ &1+b=2 a \end{aligned}$$
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