Number of Solutions

Number of Solutions

Objective: Determine the number of solutions to linear equations.

Fill in the Blank

WARMUP - Solve: -5x - 13 = 15 - 3x

​WARMUP EXPLAINED

-5x - 13 = 15 - 3x

+3x

+3x

-2x - 13 = 15

+13

+13

-2x = 28

-2

-2

x = -14

-5(-14) - 13 = 15 - 3(-14)

​Plug in -14

70 - 13 = 15 + 42

57 = 57

​There is ONE SOLUTION to this equation...-14

EXAMPLE

(No Solution)

​2x + 3 = 2x + 7

Multiple Select

What qualities are associated with "no solution" problems?

(choose ALL that apply)

• There are an infinite number of solutions.

• The variables all cancel and only constants are left.

• The final equation is ALWAYS TRUE.

• The final equation is ALWAYS FALSE.

• There is only one solution for the equation.

EXAMPLE

(Infinite Solutions)

​2x + 6 = 2(x + 3)

(Identity)

(All Real Numbers)

Multiple Select

What qualities are associated with "identity" problems?

(choose ALL that apply)

• There are an infinite number of solutions.

• The variables all cancel and only constants are left.

• The final equation is ALWAYS TRUE.

• The final equation is ALWAYS FALSE.

• There is only one solution for the equation.

"NO SOLUTION" and "IDENTITY" are often confused with equations with a solution of zero

Drag and Drop

Match the equation with the number of solutions.

16 + 6x = 2(3x + 8) ​

Placeholder

15 = 7 - 3x ​

Placeholder

2 + 4x - 12 = 4(x - 3) ​

Placeholder

Drag these tiles and drop them in the correct blank above

Identity

One Solution

No Solution

​EXAMPLE

​Given the equation: 7(x - p) = -42 + 7x

For what value of p does the equation have infinite solutions?

A) 42

B) 6

C) -6

D) 7

Multiple Choice

Given the equation:

4(x - p) = -32 + 4x

For what value of p does the equation have infinite solutions?

• 8

• 32

• 16

• 4

​EXAMPLE

​Given the equation: px - 12 + 4x = 6x - 16

For what value of p does the equation have no solutions?

A) -4

B) 2

C) 6

D) -6

Multiple Choice

Given the equation:

14x - 12 = 3x + 5 + px

For what value of p does the equation have no solution?

• 11

• 14

• 12

• 1