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Each course at Mt. Regis College is worth either 3 or 4 credits. The members of the men's swim team are taking a total of 48 courses that are worth a total of 155 credits. How many 3-credit courses and how many 4 -credit courses are being taken?

Find the equilibrium point for the following pairs of demand and supply functions. \(D(p)=760-13 p\) \(S(p)=430+2 p\)

Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If \(a\) system has no solution, state this. $$ \begin{aligned} &2 y=3 x+5\\\ &x=y-3 \end{aligned} $$

Solve each system. If a system's equations are dependent or if there is no solution, state this. $$ \begin{aligned} x-y+z &=4 \\ 5 x+2 y-3 z &=2 \\ 4 x+3 y-4 z &=-2 \end{aligned} $$

Solve using Cramer's rule. \(3 x+2 y-z=4\) \(3 x-2 y+z=5\) \(4 x-5 y-z=-1\)

Find the equilibrium point for the following pairs of demand and supply functions. \(D(p)=800-43 p\) \(S(p)=210+16 p\)

If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. Solve using the substitution method. $$ \begin{aligned} &4 p-2 q=16\\\ &5 p+7 q=1 \end{aligned} $$

Each course at Pease County Community College is worth either 3 or 4 credits. The members of the women’s golf team are taking a total of 27 courses that are worth a total of 89 credits. How many 3-credit courses and how many 4-credit courses are being taken?

Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If \(a\) system has no solution, state this. $$ \begin{aligned} 4 x-y &=9 \\ x-3 y &=16 \end{aligned} $$

Dana is designing three large perennial flower beds for her yard and is planning to use combinations of three types of flowers. In her traditional cottage-style garden, Dana will include 7 purple coneflower plants, 6 yellow foxglove plants, and 8 white lupine plants at a total cost of 93.31 dollars. The flower bed around her deck will be planted with 12 yellow foxglove plants and 12 white lupine plants at a total cost of 126.00 dollars. A third garden area in a corner of Dana's yard will contain 4 purple coneflower plants, 5 yellow foxglove plants, and 7 white lupine plants at a total cost of 72.82 dollars. What is the price per plant for the coneflowers, the foxgloves, and the lupines?