Question

systems of inequalities

Answer 1

SS?

Answer 2

??

Answer 3

y>−2
x+y≤4

Answer 4

Do you know what to do first?

Answer 5

plot

Answer 6

Good good.

Then what?

Answer 7

i dont know how to plot y>-2

Answer 8

Do you know the difference between less than and less than or equal to?

Answer 9

yes

Answer 10

y is greater that -2

Answer 11

Let me rephrase that.

Do you know the difference between the lines?

Answer 12

yes the greater than or equal to?

If its greater than or equal to/ less than or equal to it has to be a solid line

Right?

Answer 13

That is correct.

Answer 14

And what about the normal greater than?

Answer 15

dashed line

Answer 16

Correct again.

Answer 17

So y>-2 is a dashed line, we know that so far.

Where on the grid would it go?

Answer 18

im not sure

Answer 19

-2 would be the slope?

Answer 20

That wouldn't be correct because it's not in slope-intercept.

Answer 21

it would be the y intercept?

Answer 22

Yes.

Or in other words, where the line is on the grid.

Answer 23

oh there wouldnt be a slope

Answer 24

Yes.

Answer 25

so nowi shade the top because > = greater than = top/right side?

Answer 26

That is correct.

Answer 27

ok thats where i get confused, i have another example where it says y> x-2 but for that i would shade left side, why is that?

Answer 28

Let me graph that real quick.

Answer 29

I believe why that is is because there's an "x" in the problem.

Answer 30

In the original y>-2, there's no "x".

Answer 31

But in this problem/inequality, there's an "x", so that would cause the shading to switch to the left side.

Answer 32

now im not suere how to graph the second equation

Answer 33

It would still be the same line, just shaded on the left side instead of the right.

Answer 34

what

Answer 35

4 is the y-intercept in the second equation

Answer 36

im confused?

Answer 37

Please excuse my poor drawing skills.
As FexrlessRxby was explaining, one way to solve this problem would be to plot the lines (as I tried to do) and then to shade the regions of the graph, based on the sign of the inequality (shade above and to the right for "greater-than"; shade below and to the left for "less-than")
The portion where the shading overlaps would be the solution to the system.

Answer 38

And I should shade the same for this x+y≤4

Answer 39

My mistake, I graphed y >= 2, instead of y > -2, as the question asks (also, the line would be dotted, not solid, for a > sign, as opposed to >=.
The drawing still illustrates the idea, even though I got the number wrong.
The blue line and shading represents the region
y >= 2
and the green line and shading represents the region
x+y <= 4

Answer 40

how did u graph x+y≤4

Answer 41

Apologies, my drawing was not very good.

Please refer to this diagram made using Desmos graphing calculator for a clearer picture.

x + y ≤ 4 can also be rewritten as y ≤ -x + 4, if that makes it easier to visualize.
The graph would be the line y = -x + 4, with shading underneath the line, since the symbol is "≤", signifying "less than", or below the line

Answer 42

where did you get the - in y ≤ -x + 4

Answer 43

oh i forgot about that

Answer 44

but the full question was

Which ordered pair is a solution to the system of inequalities?

(1, 3)
(1, 5)
(0, −4)
(−2, −3)
doesn't that mean which of these options would be in the double shaded region

Answer 45

That's right, you would want to find out which of the points listed falls within the double-shaded region, meaning it satisfies both of the inequalities in the system

Answer 46

i was learning about this today

Answer 47

so (1,3)

Answer 48

Thank you