# Substitution to solve

#### Dominic

##### Junior Member
Use substitution to solve:

3x-y=15
5x+y=9

3x-y=15
5x+y=9
-2x+y=6

y=3

Then:

5x+3=9
9-3=6

x= 6/5

Thank you.

#### tkhunny

##### Moderator
Staff member
Dominic said:
Use substitution to solve:
3x-y=15
5x+y=9

3x-y=15
5x+y=9
-2x+y=6
Couple of things went wrong already.

1) It says "Use Substitution". That isn't substitution. Solve one equation for one variable and substitute into the other equation.

2) Are you adding the two equations or subtracting? I expected you to add them, so that -y + y = 0 and you could solve easily for 'x'. Unfortunately, you didn't get zero. Further, 3x + 5x = 8x??? 3x - 5x = -2x Oh, you subtracted that part. 15 - 9 = 6. Subtraced that part, too. So, ADD them.

3x + 5x = 8x
-y + y = 0
15 + 9 = 24

Leaving

8x + 0 = 24
8x = 24
x = 3

I have no idea how you managed y=3 from what you have.

#### Unco

##### Senior Member
G'day Dominic,

For substitution you have rearrange one of the equations to get one variable the subject e.g from equ 1, y = 3x-15; then substitute this into the second equation.

That is, the second equ becomes 5x + (3x-15) = 9

You then solve for x, and plug this value for x into either of the equations to get y.

Cheers,
Unco (avid SOSer)

Edit: Did you just delete your last post, Dominic?

#### tkhunny

##### Moderator
Staff member
Substitution Method.

Solve one equation for one variable.
3x-y=15 --> -y = 15 - 3x --> y = 3x - 15

Substitute that expression into the other equation.
5x+y=9 --> 5x + (3x - 15) = 9 --> 5x + 3x - 15 = 9 --> 8x = 24 -- x = 3

Substitute that value back into the first equation.
y = 3(3) - 15 = 9 - 15 = -6

Check

3(3)-(-6) = 9 + 6 = 15 -- Check!
5(3)+(-6) = 15 - 6 = 9 -- Check!

x = 3 and y = -6

THAT is the substitution method.

We neither added nor subtracted any equations. That's a different method.

#### Denis

##### Senior Member
Dominic said:
3x-y=15
5x+y=9
-2x+y=6

y=3
Sorry Dominic, but this is so hopelessly wrong that I can see
you need more help than you can get here...a private tutor perhaps.

#### Dominic

##### Junior Member
Sorry Dominic, but this is so hopelessly wrong that I can see
you need more help than you can get here...a private tutor perhaps.
Denis, as far as I know this is a MATH HELP FORUM not a site where to insult one another. I took your comment of being hopelessly wrong very offensive and I'd like for you to either choose your words better or just not come into my posts at all. Personal comments is not what getting help in Math is about and I believe it is quite obvious that if I knew what I was doing I wouldn't waste my time nor anybody elses' time coming to this forum. So once again, I'd appreciate it if in the future you keep your personal comments to yourself.

#### tkhunny

##### Moderator
Staff member
I don't recommend that you take comments harshly, but you may choose to do so.

I wish we could help everyone, but sometimes we have to consider that other resources might be more appropriate.

Try to remember that everyone gets an opinion.

Now, where's that next math question?

#### Denis

##### Senior Member
"Denis, as far as I know this is a MATH HELP FORUM.."

CORRECT; which means this is NOT a classroom.

"...not a site where to insult one another."

Plus I ain't typing a whole chapter of apologies...

#### Dominic

##### Junior Member
Denis said:
"Denis, as far as I know this is a MATH HELP FORUM.."

CORRECT; which means this is NOT a classroom.

"...not a site where to insult one another."

Plus I ain't typing a whole chapter of apologies...
Of course it is my business just as if I made an unethical comment dirrected towards you it would be your business! I never said this was a class room nor did I force you to post anything related to math or not in my posts. I would appreciate it if you not post anymore where you see my name because I could care less what you have to say!

#### stapel

##### Super Moderator
Staff member
Meanwhile, Denis may be correct.

Your work shows misunderstandings of such magnitude that re-teaching the material necessary for you to understand our explanations of this particular exercise is very likely beyond anything we can do through this service. As mentioned, this is a free online tutoring service, not a classroom environment. You would appear to need individualized course instruction, which we simply cannot provide here.

If you choose to take the limitations of the free service the volunteers have provided to you as a personal insult, that is your choice. And while we may regret your choice, I don't think Denis needs to apologize for it. Sorry.

Eliz.