Question

I am really stuck on this problem, i have no clue how to do it.
Solve the system of inequalities by graphing.

y > x – 6
|y|<= -6

Answer 1

are you sure about the 2nd equation ?

Answer 2

oh your right
the second equation should be positive 6

Answer 3

ok, that makes more sense

| y| will always be 0 or bigger (the | | makes what's inside positive) so it can *never* be negative.

| y | ≤ 6 means
1) if y is positive , y ≤ 6
2) if y is negative, then -y is positive, and we can write -y ≤ 6
this can be written as y ≥ -6

to find the answer, first plot the *lines*

y= x - 6
y = 6
y = -6
can you pick out those lines in the graphs you posted ?

Answer 4

kinda, my guess would be b or c

Answer 5

to plot a line, find two points on the line and draw a line through the two points.

for example,
when y= + 6
that means y is always 6 (x can be anything)
so let x=0 and we get the point (0,6)
let x = 1, and we get the point (1,6)

can you plot those two points? then draw a line through them

Answer 6

yes one sec

Answer 7

ok now what

Answer 8

now plot the line y= -6
use the same idea as for y=6 to find 2 points. Can you do that ?

Answer 9

yep one sec

Answer 10

ok done

Answer 11

now plot the last line
y= x – 6

to find 2 points, let x=0. what is y ?
then let x = 6, what is y ?

Answer 12

i made the line but what points do i plot just 0 for x and -6 for y

Answer 13

the idea is you know
y= x - 6
the means if you have a number for x, you put it in the equation
example: x=0
y= 0 - 6
0 - 6 is - 6
y = -6

that means (0,-6) is a point on the line.

now do the same thing for x=6 to find y. can you do that ?

Answer 14

ok it i put 6 in for x for the equation y=x-6 i get 0

Answer 15

yes. that means the point (6,0) is a point on that line

plot (0,-6) and (6,0)
and draw a line through them. that is the line y = x - 6

Answer 16

ok

Answer 17

now we look at the > signs

we really have
y ≤ 6
y ≥ -6
y > x – 6
the region we want satisfies these 3 relations.

Answer 18

look at y ≤ 6
we have to pick the "correct side"
to find the correct side, pick a point Example (0,0)
use the y value from (0,0) and put it into
y≤ 6
0 ≤ 6
is this true? Yes! so the point (0,0) is on the "correct side"

Answer 19

ohhh ok

Answer 20

all points below the line y= 6 are part of the answer

can you do
y ≥ - 6

is (0,0) on the correct side or the wrong side of y ≥ - 6 ?

Answer 21

the correct side

Answer 22

so far we know that the region is above the line y= -6 and below the line y=+6

finally, test
y > x – 6

is (0,0) on the correct side or the wrong side ?

Answer 23

the correct side

Answer 24

so if you plotted the lines correctly, and we shade in the correct sides, we get a picture like this