Solve the system of inequalities by graphing.
y≤-4x-2
y3x-2

Question

Solve the system of inequalities by graphing. 
y≤-4x-2
y>3x-2

anonymous · Answer

attachment

john_es · Answer

The first step I would do is plotting the lines,
$$y=-4x-2\ 
y=3x-2$$

anonymous · Answer

Okay. Then I would use substitution, right?

john_es · Answer

Yes, you can use the values x=-4,x=-2,x=-1,x=0,x=1,... then substitute in each equation and find values for y. Then plot each line. It would be as the plot I attach you.

john_es · Answer

The blue line is y=-4x-2. The magenta (or red) line is y=3x-2.

john_es · Answer

Do you understand it?

anonymous · Answer

Yes. Thank you for your help.

john_es · Answer

You're welcome ;).

john_es · Answer

One thing more. As you see, the inequalities tell you something more. When the inequality is,
$$y\leq-4x-2$$It means you must choose those values of y that are under the line y=-4x-2 (including the line we plotted). An when the inequality is,
$$y>3x-2$$It tells you that you must choose those values of y that are over the line y=3x-2 (without including the line). So the solution appears like the one you must choose.

anonymous · Answer

Thank you! I really appreciate how you explained it to me, instead of just giving me the answer.

john_es · Answer

You're welcome ;).