which of the following is a linear inequality in two variables. explain your answer.

Question

1. 3x - y > 12
2. 19 < y
3. y = 2/5 x
4. x < 2y + 5
5. 7(x-3) < 4y
6. -6x = 4 + 2y
7. x + 3y < 7
8. x > -8
9. 9(x-2) <15
10. 13x + 6 <10 -7y

Answer 1

Hi Kirsten.  Let's see what we have here. First, let's eliminate anything that only has one variable.

1. 3x - y > 12
2. 19 < y
3. y = 2/5 x
4. x < 2y + 5
5. 7(x-3) < 4y
6. -6x = 4 + 2y
7. x + 3y < 7
8. x > -8
9. 9(x-2) <15
10. 13x + 6 <10 -7y

Next, let's eliminate anything that isn't an inequality (that is, it's an equality).

 

1. 3x - y > 12
2. 
3. y = 2/5 x
4. x < 2y + 5
5. 7(x-3) < 4y
6. -6x = 4 + 2y
7. x + 3y < 7
8. 
9.
10. 13x + 6 <10 -7y

 

Now, let's eliminate anything that isn't linear (that is, has power of x or y greater that one).  Oh, everything that's left is linear.  Never mind. 

 

Well then, as to form.  Some say that linear inequalities must be of the form ax + by <> c. where <> stands for any inequality symbol.  If that is the definition you've been asked for, then some of them are not in the proper form.  We could eliminate those as well (it all depends on what your instructor is asking for).

 

1. 3x - y > 12
2.
3.
4. x < 2y + 5
5. 7(x-3) < 4y
6.
7. x + 3y < 7
8.
9.
10. 13x + 6 <10 -7y

 

What remains is numbers 1. and 7.

 

I hope that helps.

 

Regards,

Mike N.