SOLUTION: how to solve this equation x+y<5 x-y>1 by using the graphs of linear inequalities

Algebra ->  Linear-equations -> SOLUTION: how to solve this equation x+y<5 x-y>1 by using the graphs of linear inequalities       Log On


   

Question 149190: how to solve this equation x+y<5 x-y>1 by using the graphs of linear inequalities
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Plot the two lines - don't worry about the inequality yet
x+%2B+y+=+5
y+=+-x+%2B+5
x+-+y+=+1
y+=+x+-+1
graph%28600%2C400%2C+-10%2C+10%2C+-10%2C+10%2C+-x+%2B+5%2C+x+-+1%29
As you can see, the two lines cut the plane into 4 pieces.
Now let's look at the inequalities again.
x+%2B+y+%3C+5
y+%3C+-x+%2B+5
Since this equation does NOT include an equality, draw the line that is sloping downward (the slope for this line = -1) using a dashed line.
Next, since the inequality is < (less than), shade the area BELOW that line.
Do the same steps for the other line.
x+-+y+%3E+1
y+%3E+x+-+1
Since this equation does NOT include an equality, draw the line that is sloping upward (the slope for this line = 1) using a dashed line.
Next, since the inequality is > (greater than), shade the area ABOVE that line.
The answer is the area that is shaded by both. So, the area that is both BELOW the first line and also ABOVE the second line.
Remember to use dashed lines.
If you look at the plot as the letter X, the area you want is to the left of the X and NOT including the lines that make the X