1. 8-1 Solve Systems by Graphing
9P9: Solve 2X2 systems graphically

2. Possible outcomes of 2 lines
They cross (intersect) in one place:
1 solution
2) They do not cross (Parallel):
No Solution
They coincide (same equation):
infinite number of solutions

3. Why? If you want to compare to cell phone plans based
on (minutes, Cost).
What does the point where they cross represent?
Minutes and cost are the same
Which charges less per minute?
Verizon, line not as steep
How much does AT&T charge for activation? $0
AT&T
Verizon

4. Example 1: Is (1,2) solution to this system?
for y = x & x + y = 4
2 = (1) + 2 = 4
2=2 yes =4
4 = 4 yes
So (1,2) is a solution to this system

5. Example 2: Is (-3,2) solution to the system?
a + b = & b + 3a = 4
= (-3) =4
-1 = -1yes (-9) = 4
-7 = 4 no
So (-3,2) is not a solution to this system

6. Ex 3: Find Solution by graphing Hint: Find point(s) of intersection
x + y = 3 and x – y = 1
-x x
y = -x + 3
-1 + y y
x -1 = y
The solution is (2,1)

7. Ex 4: y – 2x = 3 & y = 2x - 2 +2x +2x y = 3 + 2x
Hey when they have the same slopes they are parallel and don’t cross.
That means there is no solution!!

8. Ex 5: 3y - 2x = &
+2x x
3y = 6 + 2x
Hey, these are the same line so all the points are the same or infinite # of solutions

9. Find solutions by graphing
Ex 6:
x + 2y =7 & x = y + 4
Remember to solve for y!
-x x
2y = 7- x
x - 4 = y
The solution is (5,1)

10. Assignment
8-1/ /8-28 even,32, 40-46