Classify System of Equations

How many solutions does the system of equations above have?

• one solution

• infinite many solutions

• no solution

How many solutions does the following graph have?

• infinitely many solutions

• no solution

• one solution

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

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

• Parallel lines

• the same line 

• Intersecting lines

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

Classify the system of equations

• consistent and independent

• consistent and dependent

• inconsistent