Classifying Linear Equations

What type of solution does this graph have?

• Infinite solutions

• One solution

• No solution

Categorize the descriptions and examples as No Solution, One Solution, or Infinitely Many Solutions.

Groups:

(a) No Solution

,

(b) One Solution

,

(c) Infinitely Many Solutions

• lines overlap

• parallel lines

• unequal coefficients, equal or unequal constants

• have a solution in the form of (x, y)

• same slope, same y-intercept

• different slopes

• equal coefficients, equal constants

• do not intersect

• same slope, different y-intercept

• 
• 
• 
• same line

• lines intersect in one place

• equal coefficients, unequal constants

• same equation

What is the solution to this system of equations?

• (1,4)

• (4,1)

• (3,5)

• (-1, 4)

What is the solution to this system of equations?

• (3,-3)

• (-3,3)

• (0,1)

• (1,0)

What is the solution to the equations?

• One Solution

• No Solution

• Infinite Solutions

Organize these options into the right categories.

HINT: IF THE LINES HAVE DIFFERENT SLOPES, THEY WILL INTERSECT... ONE SOLUTION

IF THE LINES HAVE THE SAME SLOPE BUT DIFFERENT Y INTERCEPTS, THEY WILL BE PARALLEL... NO SOLUTIONS

IF THE LINES HAVE THE EXACT SAME EQUATION AFTER YOU SIMPLIFY THEM, THEY WILL BE THE SAME LINE... INFINITE SOLUTIONS.

y = mx + b

Groups:

(a) No Solution

,

(b) One Solution

,

(c) Infinite Solutions

• y=2x+5
  and y=2x+7

• y=3x-2 and y=-2x+1

• y=5x+2 and y-2=5x

How many solutions?

3x -70 = 3x + 80

• One Solution

• No Solution

• Infinite Solutions

WITHOUT GRAPHING
what can you say about these lines

• Consistent and Dependent

• Consistent and Independent

• Inconsistent and Dependent

• Inconsistent and Independent

what can you say about these lines

• Consistent and Dependent

• Consistent and Independent

• Inconsistent and Dependent

• Inconsistent and Independent

WITHOUT GRAPHING
what can you say about these lines

• Consistent and Dependent

• Consistent and Independent

• Neither

• Inconsistent