Solving Matrix Equations (Week 3 COL)

Solve the following system using matrices, as in the video.
 $x-6y+4z=-12$ 
  $x+y-4z=12$  
 $2x+2y+5z=-15$  

• (0, 0, -3)

• Infinitely Many Solutions

• No Solution

• (0, 0, 0)

Solve the following system using matrices, as in the video.
 $-x-5y+z=17$  
 $-5x-5y+5z=5$  
 $2x+5y-3z=-10$  

• (-1, -4, -4)

• (1, 4, 4)

• (-1, 4, 4)

• (1, -4, -4)

How many solutions does the following system have?
 $2x-3y=-7$  
 $-4x+6y=14$  

• Infinitely Many Solutions

• No Solution

• One solution

• Two solutions

How many solutions does the following system have?

 $5x-15y=25$  

 $x-3y=15$   

• Infinitely Many Solutions

• No Solution

• One Solution

• Two Solutions

Solve the following system using matrices as in the video.
 $4r-4s+4t=-4$  
 $4r+s-2t=5$  
 $-3r-3s-4t=-16$  

• (1, -3, -1)

• (1, 3, 1)

• (-1, 3, 1)

• (-1, -3, -1)

Theater is putting on a show.

Week 1, they sold 10 student tickets, 15 adult tickets, and 5 reserved tickets for a total of $130.

Week 2, they sold 7 student tickets, 10 adult tickets, and 10 reserved tickets for a total of $134.

Week 3, they sold 25 student tickets, 7 adult tickets, and 20 reserved tickets for a total of $225.

How much is each type of ticket?

• Student: $5, Adult: $7, Reserved: $2

• Student: $2, Adult: $7, Reserved: $5

• Student: $2, Adult: $5, Reserved: $7

• Student: $3, Adult: $8, Reserved: $12

You have a jar of change.

There are 37 total coins, consisting of nickels, dimes, and quarters.

The total value of the coins is $3.75.

You also know there are twice as many nickels as dimes.

How many of each coin do you have?

• 20 dimes, 10 nickels, 7 quarters

• 10 dimes, 20 nickels, 7 quarters

• 9 dimes, 18 nickels, 10 quarters