Unit 4

Unit 4 - Linear Equations and Linear Systems

Unit 4 Vocab

Solving equations

In fact, solving an equation is just like solving a puzzle. And like puzzles, there are things we can (and cannot) do.

Here are some things we can do:

• Add or Subtract the same value from both sides
• Clear out any fractions by Multiplying every term by the bottom parts
• Divide every term by the same nonzero value
• Combine Like Terms

Number of solutions

• Most equations will have 1 solution.
  • This looks like ** X = Some Number **
  • This happens any time that the two sides of the equation have a different number of variable terms.
    • 3x+5=9
    • 3x+5=2x-4
• Some times an equation has a matching number of variable terms on each side. 🔔🔔🔔🔔🔔
  • If the variables match then they will cancel out.
    • 3x+5=3x+5
    • 3x+5=3x+2
  • In these special cases we must check the constant terms (The just numbers) on each side.
    • If they match there are infinite solutions. This means any value for x will satisfy the equation.
      • 3x+5=3x+5
      • 2x=2x
      • x+5 = x+5
    • If they do not match there is no solution to the equation.
      • 3x+5 = 3x+2
      • 2x = 2x+5
      • x+5 = x