SOLUTION: please help me graph the solutions of the system: y<2x-6 and 2x+3y<3 and find the point of intersection.

Algebra ->  Graphs -> SOLUTION: please help me graph the solutions of the system: y<2x-6 and 2x+3y<3 and find the point of intersection.      Log On


   

Question 679822: please help me graph the solutions of the system: y<2x-6 and 2x+3y<3 and find the point of intersection.
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with highlight%28y%3C2x-6%29
The y intercept is -6
Plot (0, -6)
The x intercept is where y = 0
0=2x-6
6=2x
6%2F2=x
Plot (3, 0)
Draw a dashed line through the intercepts, so at to NOT include the points on the line.
Lightly shade the area below the line, since y is <
...
Using 2x+3y<3
Isolate the y variable
3y < -2x+3
y < %28-2%2F3%29x++%2B+3%2F3
highlight_green%28y%3C%28-2%2F3%29x%2B1%29
The y intercep is 1
Plot (0,1)
The x intercept is where y = 0
0 = %28-2%2F3%29x%2B1
-1 = -2%2F3x
x = 3%2F2
Plot (3%2F2, 0)
Draw a dashed line through these intercepts. It is dashed so as to NOT include the points on the line. Lightly shade the area below the line since y is <.
...
To find the intersection, set the equations equal to each other.
2x-6+=+%28-2%2F3%29x+%2B+1
2x+%2B+%282%2F3%29x+=+1+%2B+6
%288%2F3%29x+=+7
x+=+7%283%2F8%29+=+21%2F8
Substitute this x variable into either of the equations to solve for y
y = 221%2F8 - 6 = %2821%2F4%29+-+6%284%2F4%29+=+-3%2F4
The intersection point is (21%2F8,-3%2F4)
...
The area that is shaded for both inequalities is the solution
...
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cy%3C2x-6%2Cy%3C%28-2%2F3%29x%2B1%29
.....................
Delighted to help; feel free to email if you have further questions.
HomeworkHelpers@readingboosters.com
-Reading Boosters
Website: www.MyHomeworkAnswers.com
Wanting for others what we want for ourselves.