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

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

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

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

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

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 -1 + y x -1 = y The solution is (2,1)

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!!

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

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

Assignment 8-1/ 360-361/8-28 even,32, 40-46