Exam 4: Linear Systems

Graph: 3x - 2y = 18

Find the slope of the following: 20y - 4x = 5

Solve graphically: 4x = -3y and 42 - 7y = 3x

Find the slope and y-intercept: 3x + 2y = 10

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?

Solve the system of equations: 2x + 8y = -18 2x - 4y = 10

Solve for x and y: 4x + 9y = 72 6x + 15y = 90

Solve graphically: 4x + 3y = 12 and 3x - 4y = -24

Solve the system of equations: 3x + y = 13 x - 6y = 7

A couple is about the get married. They decide to start a joint bank account to save for a house. They want to have an initial investment of $9000. The first partner contributes $350 more than three-quarters what the second partner contributes. How much does each partner contribute?

Graph: y = 8

Graph: 5x + 4y = 20

Find the y-intercept for the following: 3x - 5y = 60

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?

Find the slope and y-intercept: 1.5x + 3y = 2.4

Graph: 6x - 2y < 14

The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

Graph: x = 7

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?

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