Question

Graph the solution:

3x-y-7<0
x+5y+3>=0

This is my thought process in this:

The first equation I can solve for y since we don't have to worry what x is. And I get y>3x-7.

The second one, however, y is being multiplied by 5, so I can't just divide by 5 on both sides because I don't know if the value of y will be positive or negative (and then I'll have to switch the sign).

...So I don't know about the second equation. Help please?

Thank you!

Answer 1

x+5y+3>=0

5 y > -x -3

y > -x/5 -3/5

You divided by a positive number, so there is no reason to reverse the direction of the arrow. Now graph that line and shade above it.

Answer 2

5y ≥ -x - 3
but you are dividing by 5, so you don't have to worry about the inequality sign.
so
y ≥ -x/5 - 3/5

Now in each case, the equation becomes the boundary.
So for the first one, draw a dotted line, and shade in everything above that line.
For the second, draw a dotted line and shade in everything above that line.