Exam 4: Linear Systems

A tavern holds 50 seats. Two types of seats are available the Friday night jazz festival: stage and dining. The cost of a stage seat is $15.00 and the cost of a dining seat is $5.00. If all 50 seats are sold the tavern would collect $400.00. How many of each type of seat is available?

Alex speaks 150 words per minute on average in French, and 190 words per minute on average in Spanish. She once gave cooking instructions in French, followed by cleaning instructions in Spanish. Alex spent 5 minutes total giving both instructions, and spoke 270 more words in Spanish than in French. How long did Alex speak in French, and how long did she speak in Spanish?

Solve and find the value of x, given: = and x + 5y = 38

Solve the system graphically.

Graph: y = 8

Find the y-intercept for the following equation: 5y + 7 = 19

A machine requires 1 hours to make a unit of Product A, and 4 hours to make a unit of Product B. The machine operated for 195 hours producing a total of 80 units. How many hours were used to manufacture units of Product A?

A theatre holds 400 seats. Two types of seats are available: orchestra and balcony. The cost of an orchestra seat is $60.00 and the cost of a balcony seat is $45.00. If all 400 seats are sold the theatre would collect $22 500.00. How many of each type of seat is available?

Find the slope and y-intercept: 2x - y = 8

Graph: 6x - 2y < 14

Twice the larger number is greater than three times the smaller number by 19. The sum of the larger number plus one-third of the smaller number is 26. Find the two numbers.

A machine requires 3 hours to make a unit of Product A, and 6 hours to make a unit of Product B. The machine operated for 195 hours producing a total of 40 units. How many hours were used to manufacture units of Product A?

Find the slope of the following: x + 5y = 10

Solve graphically: 4y - 20 = 6x and x = 2