# Confused and lost

#### Dominic

##### Junior Member
I need help.

Determine whether the system has one solution, no solution, or infinitely many solutions:

y=-x+2
3x+3y=6

I'm confused and mad at myself for not knowing how to do this. I hope someone can can me.

#### Denis

##### Senior Member
Dominic said:
I need help.
Determine whether the system has one solution, no solution, or infinitely many solutions:
y=-x+2
3x+3y=6
I'm confused and mad at myself for not knowing how to do this. I hope someone can can me.
Substitute 1st in 2nd:
3x + 3(-x + 2) = 6

3x - 3x + 6 = 6

6 = 6 ... well?

#### tkhunny

##### Moderator
Staff member
It is easy to be confused on such a problem. I like to ask myself question like this, "For what value of x is 6 = 6?"

If x = 3, is 6=6? Yes
If x = -34, is 6 = 6? Yes
If x = "Purple Cow", is 6 = 6? Yes

It's not really a whole lot less confusing, but I do get some entertainment value out of it.

#### soroban

##### Elite Member
Hello, Dominic!

Determine whether the system has one solution, no solution, or infinitely many solutions:

y = -x + 2
3x + 3y = 6

I'm confused and mad at myself for not knowing how to do this. . . how to do what?
Sorry, but I have to say it: . Did you even TRY to find the solutions?
. . Or did you just sit there and say, "They didn't show me the formula for this!"

How do you find out how many solutions a system has? . . . you solve it!

The first equation is already solved for y: . y = -x + 2

Substitute into the second equation: . 3x + 3(-x + 2) .= .6 . . . and solve for x.

We get: . 3x - 3x + 6 .= .6 . ---> . 6 = 6 (?)

We can't solve for x . . . all the x's dropped out.
. . But this is good news: the value of x doesn't matter . . . the statement is true.

So the system is valid for all values of x . . . it has infinite many solutions.

#### Dominic

##### Junior Member
Sorry, but I have to say it: . Did you even TRY to find the solutions?
. . Or did you just sit there and say, "They didn't show me the formula for this!"

Soroban, Confosious once said "man who jumps to conclusions is a man who jumps off cliff". I think it's obvious that if I come here for help its because I tried to find the solution and couldn't! I am not a free loader who expects anyone to do my work for me. If I come to a HELP FORUM it is for that purpose for HELP! If you are willing to help me fine, I appreciate it, but if not keep your unrelated comments to yourself!!

I do appreciate those who have help me. It is the unsoliceted comments the upset me.After all we are here to help each other not belittle one another.

#### Denis

##### Senior Member
Dominic said:
I need help.
Determine whether the system has one solution, no solution, or infinitely many solutions:
y=-x+2
3x+3y=6
I'm confused and mad at myself for not knowing how to do this. I hope someone can can me.
That's your post, Dominic me boy; sure don't look like you tried!

You could have least have shown: 3x + 3(-x + 2) =6

#### Dominic

##### Junior Member
Denis, with all due respect it is not possible for me to try if I do not know what I am doing. I am a distance learner therefore all I have is my textbook to help me. Math is not easily self taught and I am trying my best. Like I stated before I am not a free loader I just need help. I just copied an example off my book and the book did not explain how they arrived at the solution. That is all I am asking for, someone to please explain how this equation is worked out.

#### tkhunny

##### Moderator
Staff member
I appeal to Einstein on this one. "Of course we don't know what we're doing. That's why we call it research." We could apply the sme thing to learning. Learning is not the process of doing things perfectly on the first try. Try something. Do it wrong a few times. Show us SOMETHING, even if you think it looks entirely stupid. ANYTHING you give us will help us help you. It's OK to do things wrong. These are math problems. You won't break them. Keep trying.