Intro Systems of Linear Equations

What are systems of linear equations?

• a set of two or more linear equations in the same variables

• a polynomial with three terms

• set of two or more linear inequalities in the same variables

Which is a system of linear equations?

• y = -2x - 18

  3x + 2z = 45

• -4x - 9y = 45

  y = -x

• y = x² + 4

  y = 3x - 8

• Yes

• No, it only works in the top equation.
  

• No, it only works in the bottom equation.
  

• No, it doesn't work in either equation.
  

What is criteria for a system of linear equations? (Select all that apply)

• There must be 2 or more EQUATIONS (has an equal sign).

• There must be an exponent on one of the variables.

• There can only be two variables in the system.

There are 50 donkeys and chickens on a far.  There are a total of 174 legs.  Which system below can be used to figure out how many of each animal the farm has?

• d + c = 174
  4d + 2c = 50

• d + c = 50
  4d + 2c = 174

• d + c = 50
  2d + 4c = 174

• d + c = 174
  2d + 4c = 50

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38
  2s + 3c = 52

• 3s + 1c = 38
  3s + 2c = 52

• s + c = 38
  s + c = 52

• 3s + 3c = 38
  1s + 2c = 52

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

• yes

• no

What type of solution does the following system represent?

• one solution

• no solution

• infinte solutions

What is the solution to the system of equations? 
y = 3x - 8
y = 4 - x

• (3,1)

• (1,3)

• (-3,1)

• (3,-1)

• (-1, -2)
• (-1, 2)
• (1, 2)
• (1, -2)