G8

Copyright © Swun Math (^) Grade 8 Unit 4 Lesson 10 P TE

Homework

Unit 4 · Lesson 10 : Equations: No Solution or Many

Objective: I will identify equations with many or no solutions.

Vocabulary Steps

No solution: If an equation yields a statement

that is not true, such as 2=3, then the equation

has no solution.

Infinite solutions: If an equation yields a

statement that is always true, such as 2=2, then

the equation has infinite solutions.

1. Analyze the problem.


2. Simplify: use inverse operations and combine
   like terms.
    If result is a true statement, then there
   are infinite solutions.
    If variables cancel out, unequal
   numbers remain, or you must divide by
   zero, there is no solution.

Example # 1 Example # 2

Directions: Simplify. Determine the number of solutions.

18a + 14b – 12 = 11a + 5 – 4b + 7a + 18b + 7

Solution:

• Step 1: Analyze the problem


• Step 2: Simplify the equation using inverse operations
  and collecting like terms to eliminate terms.
  18 푎푎 + 14 푏푏 – 12 = 11 푎푎 + 5 – 4푏푏 + 7푎푎 + 18 푏푏 + 7

18 푎푎 + 14 푏푏 – 12 = 18 푎푎 + 14 푏푏 + 12

− 12 = 12

• Step 3: Since the variables cancel out and unequal
  numbers remain, there is no solution.

3b + 5 + 2b = 5 + 1 b + 6b ─ b

Solution:

• Step 1: Analyze the problem


• Step 2: Simplify the equation using inverse operations
  and collecting like terms to eliminate terms.
  5b + 5 = 5 + 5b


• Step 3: Since the result is equivalent equations and will
  result in 1 = 1, then there are infinite solutions. I can see
  that both sides have the same exact terms; therefore,
  there are infinite solutions.

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Date: ___