Solve Systems by Substitution or Elimination

Solving Systems: Substitution and Simple Elimination

Poll

We covered solving systems of equations before Thanksgiving break. How confident are you in remembering that material?

• 0 - not confident at all

• 3 - kinda, maybe? I might be able to start but would get lost...

• 6 - I could probably do an "easier" example if I looked back at my notes

• 10 - give me the quiz now!

Multiple Choice

Solve the system:

$$y=x+2$$  
$$2y+x=10$$  

• (3, 5)

• (2, 4)

• (-2, 4)
  

• (3, -5)

Multiple Choice

Solve the system:

$$2x-y=2$$  

$$2x+y=6$$  

• (1, 0)

• no solution

• (2, 2)

Multiple Choice

Solve the system:

$$4x+8y=-24$$  

$$-4x-2y=-12$$  

• (6, -6)

• (6, -18)

Infinite Solutions & No Solutions

• Sometimes when solving using substitution and elimination, we are left with "weird" equations

• If an equation has 0x but is "true" we say that it has infinite solutions.

• If an equation has 0x but is "false" we say that is has no solutions.

• The picture --> shows what our work would look.

Open Ended

What method of solving (substitution or elimination) would be the EASIEST to solve if our question was the following. Why do you think that?

$$2x+5y=22$$  

$$-2x+y=2$$