8.L.a: Systems of Equations (3 methods)

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

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450
• 3x + 2y = 450
  2x + 4y = 315
• 2x + 2y = 315
  3x + 4y = 450

This system has _____ solutions

• 0
• 1
• 2
• Infinitely many

What is the solution?

• (1, -1)
• (-1, 1)
• (0, -2)
• (0, 1)

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

• (0,3)
• (3,0)
• No solution(parallel lines)
• Infinitely many solutions

Lisa and Tammy are selling items at the craft show.  Which might be a reasonable solution from the graph showing the number of items sold when they both have earned the same amount?

• (1, 12)
• (3, 19)
• (5, 25)
• (0, 10)

The solution to a system of equations is _________________. 
I.  the sum of the slopes of two lines  
II. the point where two lines intersect
III. always unique
IV. the ordered pair that makes both equations true 

• only II
• both I and II
• only IV
• both II and IV

One equation in a system of equations is y = 2x + 10. Which equation below would have to be the second equation so that the system has infinitely many solutions?

• y = 5x – 8
• y = 2x – 10
• y + 2x = 10
• y = 2(x+5)

Identify which method for solving systems is being described by this fact:

If one equation is isolated like y = 2x or

x = 7 - 4y then this method should be used.

• Graphing

• Substitution

• Elimination

Identify which method for solving systems is being described by this fact:

Equations must have like terms "stacked" up vertically, usually written in standard form.

• Graphing

• Substitution

• Elimination