SOLUTION: I don't understand the shading portion of this particular question that I have. It is 6x - y> -4 and -x + 4y less than or equal to 6. It wants me to graph and show what part of the

Question 1040380: I don't understand the shading portion of this particular question that I have. It is 6x - y> -4 and -x + 4y less than or equal to 6. It wants me to graph and show what part of the graph needs to be shaded.
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
6x - y> -4 and -x + 4y less than or equal to 6

and

----------the system based on two linear inequality relationships; y is unequal to two defined expressions.

Draw the "line" for 6x+4 but make a DOTTED line and shade the region UNDER the "line"; draw the SOLID line for x/4+3/2 AND shade the region ABOVE the line. You can make this look right on paper. It will not be as easy to see in this web page.

This graph here is NOT complete!

Neither is this one!
-----only the upper right region should be shaded. The red line here is to be the dotted one, and the green line should be the solid one.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
6x - y > -4
-x + 4y <= 6

first you want to solve for y in both equations.

first inequality:
start with 6x - y > -4
subtract 6x from both sides of the equation to get -y > -4 - 6x.
multiply both sides of the inequality by -1 to get y < 4 + 6x.
reorder the terms in descending order of degree to get y < 6x + 4.
note that multiplying or dividing both sides of an inequality by a negative number reverses the inequality.
in this case we multiplied both sides of the inequality by a negative number.

your first inequality becomes y < 6x + 4.

second inequality:
start with -x + 4y <= 6
add x to both sides of the inequality to get 4y <= 6 + x.
divide both sides of the inequality by 4 to get y <= (6+x)/4.
reorder the terms in descending order of degree to get y <= (x+6)/4.

your second inequality becomes y <= (x+6)/4.

your inequalities are now:

y < 6x+4
y <= (x+6)/4

you would graph the lines created by these inequalities.

in other words, you would graph:

y = 6x+4
y = (x+6)/4

that graph is shown below:

you would then shade the areas indicated by the inequalities.

y < 6x+4 would have the area underneath and to the right of it shaded.
since the inequality is < rather than <=, you would create a dashed line rather than a solid line.

y <= (x+6)/4 would have the area underneath and to the right of it shaded.
since the inequality is <=, you would create a solid line rather than a dashed line.

dashed line means the inequality does not include the line.
solid line means the inequality does include the line as well.

here's the graph of the inequality.
the darkest shaded area is the shaded area you would need to create manually.
that becomes the region of feasibility.
it is below the line of y = 6x + 4 but does not include that line.
it is below the line of y = (x+6)/4 and does include that line.

here's a reference on graphing inequalities.

http://www.mathsisfun.com/algebra/graphing-linear-inequalities.html
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