Question

A system of linear inequalities is shown below:

y ≥ -2x - 2
y + x ≥ 0

Describe the steps to graph the solution set to the system of inequalities.

Answer 1

@phi

Answer 2

to do these problems, you need to be able to graph a line
given its equation
for example, can you graph the line y= -2x-2 ?

Answer 3

yes i can graph using geogebra

Answer 4

it might help if you graph it.

Answer 5

i graphed it but i don't see how it would help with getting the steps to do it

Answer 6

next, you look at the relation
y ≥ -2x - 2

as you know , there are two sides the line.
we want the side "above" the line.

if that is not clear, I choose a simple point like (0,0)
does (0,0) make the relation true ? any idea ?

Answer 7

refresh your browser if that did not display properly

Answer 8

sorry something happened

Answer 9

and i don't understand it

Answer 10

\[ y \ge -2x -2 \]
does (0,0) make the relation true ?
in other words, with x=0 and y=0:
\[ 0 \ge -2 \cdot 0 - 2 \]
is this true ?

Answer 11

no

Answer 12

i think

Answer 13

simplify the right side (and pay attention to order of operations, multiply before add/subtract)

Answer 14

yes its true

Answer 15

what did you get for the right side ?

Answer 16

-2

Answer 17

ok, and yes 0 is bigger than -2, so the relation is true.

all of that means is that the point (0,0) is the "correct side" of the line
shade in the area on the side of the line that contains (0,0)

so far, so good?

Answer 18

umm sorry again openstudy is giving me problems and yes so far so good

Answer 19

@phi so what next?