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Question 159004: .. PLEASE HELP ME SOLVE THIS EQUATION.
x+y<8
2x+y<10
x>0,y>0
....
x+y<8
-x -x
________
Y<-x+8
2x+y<10
-2x -2x
____________
y<-2x+10
.. i need to graph this but i do not know how to do it.!!=S
Found 2 solutions by midwood_trail, gonzo:
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! Visit the link below.
It will help learn how to graph the inequalities.
Go to:
http://www.purplemath.com/modules/syslneq.htm
If you do not understand the link, write back.
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! the problem to be solved is:
x+y<8 and 2*x+y<10
where x and y both have to be greater than 0.
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to solve for x and y, solve for equality rather than inequality first.
you get
x+y=8
2*x+y=10
subtract second equation from first equation and you get
x = 2
if x = 2, then y = 6
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for both equations to be equal with the same values of x and y in each, x must = 2 and y must = 6.
that would be the intersection of the 2 lines on a graph.
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going back to the original inequality for x+y to be < 8, the combination of x + y must be smaller than 8. if x = 7, then y must be smaller than 1. if y = 7, then x must be smaller than 1.
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going back to the original inequality for 2*x + y < 10, the combination of 2*x + y must be smaller than 10. if x = 4, then y must be smaller than 2. if y = 8, then x must be smaller than 1.
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example:
let x = 1 and y = 2.
x+y = 3 < 8 checks out ok.
2*x+y = 4 < 10 checks out ok.
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example:
let x = 1 and y = 8
x+y = 9 not < 8 - doesn't satisfy the equation.
2*x + y = 10 not < 10 - doesn't satisfy the equation.
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viewing this on a graph should help to make it clearer.
to make the graph, we go back to the equations showing equality again.
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first equation:
x + y = 8
convert to slope-intercept form (y = m*x + b)
y = (-x) + 8
slope is -1
y-intercept is 8.
when x = 0, y = 8
when y = 0, x = 8
we have two points that we can plot to create the graph.
they are (0,8) and (8,0)
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second equation:
2*x + y = 10
convert to slope-intercept form (y = m*x + b)
y = (-2*x) + 10
slope is -2
y-intercept is 10
when x = 0, y = 10
when y = 0, x = 5
we have two points that we can plot to create the graph.
they are (0,10) and (5,0)
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graph looks like the following.
please scan below the graph for more comments.
if x has to be greater than 0 and y has to be greater than 0, the answer you are looking for appears to be the area under the graph of y = (-2*x)+10 for x = 2 to 5, and the area under the graph of y = (-x)+8 for x = 0 to 2.
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to prove this, take 2 points that don't fall within the specified areas but still fall within the areas of either curve.
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let x = .5, and y = 8.
then x + y < 8 becomes .5 + 8 which is not < 8 so it fails the test.
let x = 6, and y = 1.
then x + y < 8 becomes 6 + 1 < 8 which is ok for the first equation.
but, ........
2*x + y < 10 becomes 12 + 1 which is not < 10 so it fails the test.
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since the values of x and y must satisfy both equations, if the values satisfy one equation and not the other, the test fails.
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to prove a positive, let x = something in the specified area.
let x = 1.9 and y = 6.
x + y < 8 becomes 1.9 + 6 < 8 which is ok for the first equation.
2*x + y < 10 becomes 3.8 + 6 < 10 which is ok for the second equation.
since it passes the test for both equation, that value is good and it does fall within the specified area.
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the specified area is ...............................
the area under the graph of y = (-2*x)+10 for x = 2 to x = 5, and
the area under the graph of y = (-x)+8 for x = 0 to 2.
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