Housekeeping

Unit 2: Lesson 7Classification of

Solutions

• Students know the conditions for which a linear equation will have a unique solution, no solution, or infinitely many solutions.

Review A solution to an equation is a value you can substitute in for the variable that makes the

equation true.

Did you know that some equations have more than one

solution or no solution?

Consider the following equation: 2(x + 1) = 2x − 3. What value of x makes the equation true?

What’s the solution?

Solve each of the following equations for x.

1. 7x – 3 = 5x + 52. 7x – 3 = 7x + 53. 7x – 3 = -3 + 7x

Solve each of the following equations for x.

1. 7x – 3 = 5x + 5

Solve each of the following equations for x.

2. 7x – 3 = 7x + 5

Solve each of the following equations for x.

3. 7x – 3 = - 3 + 7x

7x – 3 = 5x + 5 7x – 3 = 5x + 5 7x – 3 = - 3 + 7x

One or None

X + 5 = 8 10 = 2x

2X = X

One Solution Equations!

x + 1 = x + 4

No Solution Equations!

2x + 3 = 2x + 5

variable terms: same

constants: different

variable terms: on one side or different

constants: same or different

What’s an Identity Equation?

X + 2 = X + 2

s + 48 = 48 + s

7y = 7y n - 10.9 = n - 10.9

3.14 r2 = 3.14 r2

PENCILS PENCILS=

=

3z = z + z + z

6(b-5) = 6(b-5)

Identity equations are equations that are true no matter what value is plugged in for the variable. If you simplify an identity equation, you'll ALWAYS get a true statement.

Infinite Solution Equations!variable terms: same

constants: same

identity statement = infinite solutions

Match the Solution to the Description!

variable terms: same

constants: same

variable terms: same

constants: different

One Solution

No Solution

Infinite Solutions variable terms: usually only one

constants: different

Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary.

11x – 2x + 15 = 8 + 7 + 9x

Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary.

3(x-14) + 1 = -4x + 5

Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary.

-3x + 32 – 7x = -2(5x + 10)

Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary.

12

(8 𝑥+26 )=13+4 𝑥

Write two equations that have no solution

Write two equations that have one unique solution each

Write two equations that have infinitely many solutions

• We know that equations will either have a unique solution, no solution, or infinitely many solutions.

• We know that equations with no solution will, after being simplified on both sides, have coefficients of x that are the same on both sides of the equal sign and constants that

are different.• We know that equations with infinitely many solutions will, after being simplified on both sides, have coefficients of x and constants that are the same on both sides of the equal sign.

Wrap Up

What now? IXL Skill U.12