Need some help!! Solve the system of inequalities by graphing on a graph at the end.
−3x − 5y

Question

Need some help!! Solve the system of inequalities by graphing on a graph at the end.
	−3x − 5y < −3
	x + 2y ≥ 2

ranga · Answer

To graph them, first replace the inequality sign with an equal sign and draw the boundary lines.

-3x - 5y = -3
x + 2y = 0

To draw the line: -3x - 5y = -3
put x = 0, find y  (that is the y-intercept)
put y = 0, find x (that is the x-intercept)

Put x = 0:   0 - 5y = -3
y = 3/5 = 0.6 (graph cuts the y-axis at y = 0.6)

Put y = 0:   -3x - 0 = -3
x = 1  (graph cuts the x axis at x = 1)

locate the point x = 1 on the x-axis and y = 0.6 on the y-axis and draw a line through them.

Do the same to plot the other line.

ranga · Answer

x + 2y = 2  in the 4th line above.

anonymous · Answer

I think I get it now actully

ranga · Answer

Since the first inequality is:  −3x − 5y < −3 
Because it is a less than sign, the plot of this line should be a dashed line (that is, not continuous).  Points on the line are not included in the solution set.  Find out which region, that is, is the region above the line the solution set or the region below the line, the solution set?  To do that choose a convenient point such as (0,0), put it in the inequality and see if it satisfies the inequality.  Then you can figure out which region is the solution set for this inequality.  Shade the region that is the solution.

For x + 2y ≥ 2
because of the grater than or EQUAL sign, the line should be continuous.  Points on the line will satisfy the inequality.  Once again pick a test point and find which side of the line the solution lies.  Shade that region.  

The region that satisfies both inequalities is the solution set for the two inequalities.

anonymous · Answer

ohhhh I get it now. That was a really good explanation !!

ranga · Answer

Thanks. If you want to see what the graph and shaded regions look like, you can copy and paste each of the two inequalities on the left, one per line, and it will graph it for you. Go to this link: https://www.desmos.com/calculator −3x − 5y < −3 (copy and paste on line 1 on the left column) x + 2y >= 2 (copy and paste on line 2 on the left column)