Classifying Solutions to Systems

Without graphing, classify each system as independent, dependent, or inconsistent.
-3x + y = 4
3x - y = 1

• Independent
• Dependent
• Inconsistent

Without graphing, classify each system as independent, dependent, or inconsistent.
x - 3y = 2
4x - 12y = 8

• Independent
• Dependent
• Inconsistent

Solve the system by substitution.
x + 12y = 68
x = 8y - 12

• Infinite Solutions
• (20, 4)
• (4, 20)
• No solution

Solve the system by substitution.
y = 2x - 1
3x - y = -1

• Infinite Solutions
• (-5, -2)
• (-2, -5)
• No solution

How many solutions does this system of equations have?

• One Solution
• No solution
• Infinitely Many Solutions
• Two Solutions

If a system of linear equations has one solution, what does this mean about the two lines? 

• Parallel lines
• the same line 
• Intersecting lines

This system has _____ solutions

• 0
• 1
• 2
• Infinitely many

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos

  m: # of glasses of milk

• t: Cost of each taco

  m: Cost of each glass of milk

• t: total cost

  m: # of food items

• t: Cost of each glass of milk

  m: Cost of each taco

What is the solution to the system?
8x + 4y = 12
y = -2x + 3

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

If a system of linear equations has one solution, what does this mean about the two lines? 

• Parallel lines
• the same line 
• Intersecting lines