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.
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
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
• 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
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