3 X 3 Systems With Matrices

How many equations are in a 3x3 system of linear equations?

• 1

• 2

• 9

• 3

Which of the following is an example of a 3x3 system of linear equations?

• x + 2y = 10

  y - 8z = 4

  -x + 3y + z = 12

• 5x + y = 9

  z = 3y

• -7x + 2y = 5

  8x + y = 0

• -6x² - y = 4

  y = 9x

  x² + 10y = 19

is any system whose equations only contain constant or linear terms. Each term can only have one variable (or no variable), and its power can only be 1.

• System of quadratic equations

• System of linear equations

• Elimination Method

• Solution

When the graphs of the three equations (three planes) intersect at a single (x, y, z) coordinate in space. This would mean that there is

• one solution to the consistent, independent system.

• Infinitely Many Solutions

• No Solution

Find the solution of the following system of equations.

2x+5y+2z=−38

3x−2y+4z=17

−6x+y−7z=−12

• (1,0,9)

• (-3,-8,2)

• (3,-8,-2)

• (3,8,-2)

A piggy bank contains only nickels, dimes and quarters. Given the following information determine the equations that will help you to find how many of each type of coin are in the bank. If

• The coins total $4.50.

• There are 32 coins in the bank.

• The number of nickels and dimes together is 8 more than the number of quarters

• 0.08n + 0.12d + 0.26q = 4.50

  n + d + q = 32

  n + d - q = 8

• 0.05n + 0.10d + 0.25q = 4.50

  n + d + q = 32

  n + d - q = 8

• 0.05n + 0.10d + 0.25q = 4.50

  n + d + q = 32

  n + d +q = 8

If a system of equations has no solution, what does the graph look like? 

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

Give the solution to the system.

• (3,1)
• (1,3)
• (-1,3)
• (1, -3)