Solving Systems of Equations

Systems of Equations

Solving by Substitution

Steps 1 & 2

Solving by Substitution

Steps 3 & 4

The solution is (42,-12)

Solving by Substitution

Example 2

Solving by Elimination

Steps 1 & 2

Solving by Elimination

Steps 3/4 & 5/6

The solution is (2,4)

Solving by Substitution

Example 2

Multiple Choice

• $\left(1,2\right)$
  

• $\left(1,-2\right)$
  

• $\left(-1,-1\right)$
  

• $\left(-1,1\right)$
  

Multiple Choice

•  $-\frac{4}{3}$ 
  

•  $\frac{2}{3}$ 
  

•  $\frac{4}{3}$ 
  

•  $\frac{22}{3}$ 
  

Number of Solutions

Most systems have one solution, but occasionally they can have Infinitely Many solutions or No solutions.

This only happens when both variables cancel

Infinitely Many Solutions

Variables both cancel, and the remaining constants are equal

No Solutions

Variables both cancel, and the remaining constants are unequal

Multiple Choice

• Zero

• Exactly One

• Exactly Two

• Infinitely Many