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Question 810829: Would you please help me get the point of intersection for the following
3x+10y>30 and -5x-5y>25
Thank you so much.
Answer by Charles3475(23)   (Show Source):
You can put this solution on YOUR website! Would you please help me get the point of intersection for the following
3x+10y>30 and -5x-5y>25
You have assumed the solution is a point of intersection. Perhaps not! Let’s find out.
Change first equation to slope-intercept form:
3x+10y>30
Subtract 3x from both sides
10y>-3x+30
Divide both sides by 10
y>-3/10 x+3
Change second equation to slope-intercept form:
-5x-5y>25
Add 5x to both sides
-5y>5x+25
Divide both sides by -5
y<-x-5
Notice I switched the inequality when I divided by a negative.
Now you have two inequalities that are graphed below:
You can graph here:
http://www.quickmath.com/webMathematica3/quickmath/graphs/inequalities/advanced.jsp
One inequality is for the region above the first line. The other is the region below the second line. The solution is where the two regions overlap. Each point within the overlap is a solution to both equations and is a point of intersection. There are an infinite number of intersections.
If you ignore the inequalities and pretend we are dealing only with simple line equations, the point of intersection occurs when you set the equations equal to each other:
-3/10 x+3=-x-5
Multiply both sides by 10
-3x+30=-10x-50
Add 10x to both sides
7x+30=-50
Subtract 30 from both sides
7x=-80
Divide both sides by 7
x = -80/7 = -11 3/7
y = 45/7
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