1. Solving Systems of Equations by Graphing

2. First figure out what your two equations are:

3. First figure out what your two equations are:
When you have a word problem, try to write out an equation.

4. First figure out what your two equations are:
When you have a word problem, try to write out an equation.
Draw a picture if you can.

5. Find the point of intersection:
Mr. Alexander rides his BMX bike off a cliff wearing a funny hat. The cliff is 1000 feet high. He falls at a rate of 3 feet per second. Mr. Lothamer jumps out of an airplane that is feet high. Mr. Lothamer falls at a rate of 7 feet per second. How high up will the two be when they can give each other a high five?
How long will it take for them to be able to give each other a high five?

6. Draw out the picture:

8. Find the Point of Intersection:
Mr. Alexander drives from his house towards Las Cruces at a rate of 60 miles per hour. He is wearing a funny scarf.
Mr. Lothamer is going the same direction riding his horse at a rate of 13 miles per hour. Mr. Lothamer starts off 25 miles from Mr. Alexander’s house towards Las Cruces.

9. Find the Point of Intersection:
Mr. Alexander drives from his house towards Las Cruces at a rate of 60 miles per hour. He is wearing a funny scarf.
Mr. Lothamer is going the same direction riding his horse at a rate of 13 miles per hour. Mr. Lothamer starts off 25 miles from Mr. Alexander’s house towards Las Cruces.
At what distance from Mr. Alexander’s house will the two meet? How much time will it take them to get to that point?

10. Draw out the picture.

11. Find the solution:
Suppose you are testing two fertilizers on bamboo plants A and B, which are growing under identical conditions. Plant A is 6 cm tall and growing at a rate of 4 cm/day. Plant B is 10 cm tall and growing at a rate of 2 cm/day. Write a system of equations for the two. Find the point when the two will be the same height.

12. Special Cases:

13. Special Cases:
If the two never meet, then we say there is “no solution”.

14. Special Cases:
If the two never meet, then we say there is “no solution”.
These are parallel lines.

15. Special Cases:
If the two never meet, then we say there is “no solution”.
These are parallel lines.
The two slopes are the ____________.

16. Special Cases:
If the two never meet, then we say there is “no solution”.
These are parallel lines.
The two slopes are the ____________.
If the two are always on each other we say there are “infinitely many solutions”.

17. Special Cases:
If the two never meet, then we say there is “no solution”.
These are parallel lines.
The two slopes are the ____________.
If the two are always on each other we say there are “infinitely many solutions”.
This means the lines are on top of each other.

18. Special Cases:
If the two never meet, then we say there is “no solution”.
These are parallel lines.
The two slopes are the ____________.
If the two are always on each other we say there are “infinitely many solutions”.
This means the lines are on top of each other.
When two lines are on top of each other the slopes are the __________ and the y-intercepts are the ____________.