What is the solution to a system?

The point where your two lines intersect is the solution. It has an x AND y

(x,y)

What methods did we use to solve?

• Graphing

• Substitution

• Elimination

With graphing, we know....

• Lines intersect- solution is: (x,y)

• Lines are parallel- NO SOLUTION

• Lines are same: INFINITELY MANY SOLUTIONS

With substitution:

• If #=# is a true statement, then INFINITELY MANY SOLUTIONS (example: 5=5)

• If #=# is a false statement, then NO SOLUTION (example: -7=2)

DON'T FORGET!!!!

• Your solution is a pair (x,y), not just x or y

• Always plug in the value you found for x or y into EITHER equation to find the other variable value.

• Example, x=3-y and 3y+x=5. If y=1, what is x?

Elimination

• Line up equations (rearrange if need be)

• Pick a variable (either x or y) to eliminate or cancel

• Make coefficients are SAME number, OPPOSITE sign. Example: 2x and -2x

Go to link in and Watch from: 6:20-9:50

https://www.youtube.com/watch?v=Tkrqrfkznoo