which ordered pair is a solution for 6x+3y>15

Question

What ordered pair is a solution for 6x+3y>15?

Answer 1

Hi Linda,

 

 

   What ordered pair is a solution for 6x+3y>15?

 

 

  One good way to solve this is to graph the inequality.

First we need to put the equation into slope-intercept form:

 

6x+3y>15

 

Add -6x to both sides

 

3y>-6x+15

 

Divide each term by 3:

 

y>-2x+5

 

The slope is -2 and the y-intercept is 5.  When graphing the line will be dashed.  Why? 

Because the line is not included in the solution set.

After graphing the line, you see that there are two areas: one above the dashed line and one below.

 

Now, choose any point to test if it is part of the solution set.

 

I choose point (0,0)

 

Substitute the point into inequality.

 

y>-2x+5

0>-2(0)+5

0>5          

Is this a true statement?  Is zero greater than 5? 

No, so this point and all other points on the same side are not part of the solution set of this inequality.

 

 

The solution set for this inequality is infinite.

To answer this question, pick any point in the area

 

I choose point (3,0).

Let's see whether it is one of the solutions.

y>-2x+5

0>-2(3)+5

0>-6+5

0>-1    The statement is TRUE so point (3,0) is part of the solution set.

 

Note:  This is only one of the points in the solution set.  Other points in the solution set are (0,6), (4,0), (3,2), (5,7).

 

ANSWER:  There are infinite solutions to this inequality.  One specific solution is point (3,0).

 

We're finished!

 

Answer 2

First, you should realize that the inequality:

     6x + 3y > 15

is exactly the same as the inequality:

     2x + y > 5

because one of the rules of inequalities is that you may divide both sides by the same positive number and retain the sense of the inequality (note: dividing by a negative number reverses the sense of the inequality).

 

Now realize that the ordered pairs are given in (x,y) form.  So, for example, (4,3) means that x=4 and y=3.

 

So, it is really easy to do the math now.

 

Here are some examples:

   Is  (2,1) a solution to 6x+3y>15?

                         6(2)+3(1)>15?

                          12 + 3 > 15?

                               15>15  ?  no, they are equal

   Is (2,2) a solution to 6x+3y>15?

                        6(2)+3(2)>15?

                          12 + 6 >15?

                              18 > 15 ? yes

 

If the question gives choices, just plug in the values for (x,y) and choose the correct answer.

 

Note: you could use the original inequality (6x+3y>15) of the reduced one (2x+y>5) and get the same equalities for (2,1) and (1,2).