Which of the following points lie in the solution set to the following system of inequalities? y> -3x+3 y> x+2 answer choices : (2,-5) (-2,5) (2,5) (-2,-5)

The point which will lie in the solution set to the following system of inequalities is:

                          (2,5)

The system of inequality is given by:

       y>-3x+3(1)

and  y>x+2(2)

Now, the point that will lie in the solution set to the following system of inequality are the point that satisfies both the inequality.

a)

 (2,-5)

when x=2 and y= -5

then by first inequality we have:

-5>-3×2+3

i.e.

-5>-6+3

i.e.

-5>-3

which is a false identity.

This means that the point will not lie in the solution set.

b)

(-2,5)

when x= -2 and y=5

then  by first inequality we have:

5>-3×(-2)+3

i.e.

5>6+3

i.e.

5>9

which is a false identity.

Hence, option: b is incorrect.

c)

(2,5)

when x=2 and y=5

then by first inequality:

    5>-3×2+3

i.e.  5>-6+3

i.e.  5>-3

which is true

and by second identity:

      5>2+2

i.e.  5>4

which is again true.

Hence, (2,5) lie in the solution set.

d)

(-2,-5)

when x= -2 and y= -5

then by first inequality we have:

-5>-3×(-2)+3

i.e.

-5>6+3

i.e.

-5>9

which is a false identity.

Hence, the point (-2,-5) do not lie in the solution set.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

step-by-step explanation:

6.48/4 4 goes into 6.48 1.62 times