SOLUTION: solve each inqualities by graphing. x>5 y<4 -

Question 124485This question is from textbook Algebra
: solve each inqualities by graphing.
x>5
y<4
- This question is from textbook Algebra

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of inequalities

In order to graph this system of inequalities, we need to graph each inequality one at a time.

First lets graph the first inequality
In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign).
So lets graph the line (simply draw a vertical line through )
graph of
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point

Substitute (0,0) into the inequality
Plug in and
Simplify

(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.)

Since this inequality is not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line
Graph of with the boundary (which is the line in red) and the shaded region (in green)
(note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
---------------------------------------------------------------

Now lets graph the second inequality
In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign).
So lets graph the line (simply draw a horizontal line through )
graph of
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point

Substitute (0,0) into the inequality
Plug in and
Simplify

Since this inequality is true, we simply shade the entire region that contains (0,0)
Graph of with the boundary (which is the line in red) and the shaded region (in green)
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
---------------------------------------------------------------

So we essentially have these 2 regions:

Region #1
Graph of

Region #2
Graph of

When these inequalities are graphed on the same coordinate system, the regions overlap to produce this region. It's a little hard to see, but after evenly shading each region, the intersecting region will be the most shaded in.

Here is a cleaner look at the intersection of regions

Here is the intersection of the 2 regions represented by the series of dots
RELATED QUESTIONS
Directions : Solve each system by graphing (graphing and by Substitution Y = x -... (answered by checkley79)

Solve each system by graphing, if possible { x - y = 4 ( 2x + y =... (answered by josgarithmetic)

Solve each system by graphing. x > 2 + y y>1 (answered by Boreal)

Solve by graphing -2x+y=4... (answered by algebrahouse.com)

solve each system by graphing. problem: y = 7x + 4 and y = - x -... (answered by jorel1380)

Solve each systen of equations by graphing. X+y=4... (answered by richwmiller,Fombitz)

Solve each system of equations by graphing. (x+y=4 (answered by mananth)

Solve each equation by graphing: (x + y = 4 (x -y = -... (answered by Fombitz,tutoringisfun)

solve each system by graphing. y=-1... (answered by checkley77)