Math HW Problem Help Please!?

Question

Does anyone know how to do this?

I just need help on this one problem, but here are the instructions...

Instructions: Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.

Problem:

x/6 - y/2 = 1/3

Thank you so much if you can help me out.

Answer 1

The equation x/6 -y/2 =1/3 is not a system. If you have two variables then you need two equations to have a system. This is a linear equation. If you graph it you would get a line. So there is an infinite number of solutions to solve it. I would first of all multiply each term by 6 and cancel and get x - 3y =2; change this to be x = 2+ 3y. Then make a table of points.

Let y = 1, then x =5 (5,1)
Let y = 2, then x= 8 (8,2)
Let y = 0, then x =2 (2,0)
Let y = -1, then x= -1 ((-1,-1)

You could keep on doing this infinitely. If you try subbing these paris of numbers in your original equation, you will get all true statements. If you graph these as pairs of points in the (x,y) form on a graph you will get a straight line.

Systems with infinitely many solutions are equations which are really the same, but one is a multiple of the other.

Take x + y = 5 and multiply each term by any number, say 2 and get the equationg 2x + 2y =10. These two equations represent a set whose solution is an infinite set of ordered pairs. If you graph them you get one line landing on top of the other one so that they are said to coincide. In set notation you woud write
{(x,y)| x + y =5}

For no solutions, when the lines are graphed you get parallel lines. They have the same slope. For example,2x - 5y =3 and -4x + 10y = 3. If you multiply the first equation by(- 2) you get -4x+10y =-6. If you inspect the 2 equations closely you see that the coefficients of the x and y terms are the same but the constants are different. If you put the two equations in slope-intercept form you would see that the slopes are the same, but the y-intercepts are different. That makes the lines parallel and you simply put down the symbol for the null set.

Answer 2

x=1 and y=3

1/6 - 3/6 ==2/6 or 1/3

Answer 3

Pi = C/d the place C = circumference and d = diameter. Then C=d*pi So C = a million.seventy 5 * 22/7 (vale of pi =22/7=3.142857...) SO the circumference is 55.5. i'm hoping that 5.5 you measured became in inches, in any different case merely degree it returned with a ruler that has inches.