Classifying Solutions to Linear Equation

Determine the number of solutions to:
6x + 3 = 15

• One solution: when x = 2

• This is never true

• This is always true (infinite number of solutions)

Tags

CCSS.8.EE.C.7A

Determine the number of solutions to:
12 - x = 15

• One solution: when x = -3

• This is always true (infinite solutions)

• This is never true

Tags

CCSS.8.EE.C.7A

Determine the number of solutions to:
3(x + 4) = 3x + 4

• One solution: when x = 0

• This is always true (infinite solutions)

• This is never true

Tags

CCSS.8.EE.C.7A

Determine the number of solutions to:
x/2 = 6

• One solution when x = 12

• This is always true (infinite solutions)

• This is never true

Tags

CCSS.6.EE.B.7

• (10,0)

• (2,12)

• (1,11)

• (0,10)

Tags

5.4C

Organize the equations according to the number of equations for each.

Groups:

(a) Infinite Solutions

,

(b) One Solution

,

(c) No Solution

• 3(x+2)=3x+6

• 3(x+4)+5=2x

• -4(x-3)+2x=-2x

• 5x+6=5x-3

• -2x-7=-2x-7

• 3x=-6

Tags

CCSS.8.EE.C.7A

How many solutions?

5y-15=5(y-2)

• No Solution

• One Solution

• Infinite Solutions

Tags

CCSS.8.EE.C.7A

How many solutions?

3 (10x + 2) = 30x + 6

• One Solution

• No Solution

• Infinite Solutions

Tags

CCSS.8.EE.C.7A

How many solutions?

12(y+2)=6(2y+4)

• No Solution

• One Solution

• Infinite Solutions

Tags

CCSS.8.EE.C.7A

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=5x+2 and y-2=5x

• y=3x-2 and y=-2x+1

Tags

CCSS.8.EE.C.8B