SOLUTION: Explain, in complete sentences, how you would use the graphing method to solve the following system of inequalities and what the final solution will look like on the coordinate pla

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Question 548977: Explain, in complete sentences, how you would use the graphing method to solve the following system of inequalities and what the final solution will look like on the coordinate plane.
x+-+2y+%3E=-8
7x+%2B+y+%3C+-6+

Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
x+-+2y+%3E=-8
Putting this into y=mx+b form we get:
x+-+2y+%2B2y%2B8%3E=-8%2B2y%2B8
x%2B8%3E=2y
%28x%2B8%29%2F2%3E=2y%2F2
x%2F2%2B8%2F2%3E=y
x%2F2%2B4%3E=y
And graphing the line
y=x/2+4:
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%2F2%2B4%29
Taking points from both above the line and under the line, we see that the points below the line agree with the inequality we started with.



7x+%2B+y+%3C+-6+
Putting this into y=mx+b form:
7x+%2B+y+-7x%3C+-6+-7x
y%3C-7x-6
And graphing the line
y=-7x-6:
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-7x-6%29
Taking points from both above the line and under the line and substituting them into the equality above, we see that the points below the line satisfy the inequality we started with.

When we graph both the lines together, the points that lie below BOTH lines are the solutions:
graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-7x-6%2Cx%2F2%2B4%29