Slide 2:
Given the system:
y < 2x – 5
2x – 4y > 6 possible solutions are: (4,0) 0 < 2(4) – 5 AND 2(4) – 4(0) > 6 (6,-2) -2 < 2(6) – 5 AND 2(6) – 4(-2) > 6 (2,-7) -7 < 2(2) – 5 AND 2(2) – 4(-7) > 6 There are MANY more solutions!! So to represent the
Solutions, we use a graph!
Slide 3:
Solve the system: First, graph each line: For x – 2y < 6, I would suggest using intercepts. x-int: (y = 0)
x – 2(0) = 6
x = 6 y-int: (x = 0)
0 – 2y = 6
-2y = 6
y = -3 The graph is a dashed line because of the “<“. Choose a test point.:
0 – 2(0) < 6
This is true so shade
to cover (0,0).
Slide 4:
Now graph For this line I would suggest using slope and y-intercept. Slope =
Y-intercept = 5 The line is solid. Choose a test point: (0,0)
0 < -3/2(0) + 5
This is true ,so shade to cover (0,0).
Slide 5:
Now merge the two graphs. The solution is the
points in the
“overlapped” region.
Slide 6:
Graph the system: y < 4 Is a horizontal line
through y – 4 – dashed and
shaded down Is the absolute value
graph shifted 3 units right –
solid and shaded away from
(0,0)
Slide 7:
Together the system is: The solution is the ordered pairs in the “overlapping” triangle.