# Solve the system of equations

G

#### Guest

##### Guest
2x – y = 5
3x + 2y = 2
2x-y=5
-2x -2x
y=-2x+5

3x+2(2x+5)=2
3x+4x+10=2
7x+10=2
-10 -10
7x=-8
7 7

x=8/7

2(8/7)-y=5
16/7-y=5
-16/7 -16/7
-y=5-16/7 I'm stuck!!

#### stapel

##### Super Moderator
Staff member
Why are you stuck? Simplify the expression "5 - 16/7" to obtain a value for y.

Eliz.

G

-y=5-16/7

-y=4 1/7
-1 -1
y=-4 1/7?????

#### stapel

##### Super Moderator
Staff member
I don't understand your question. You're okay with x being a fractional value, but not y...?

Eliz.

G

#### Guest

##### Guest
solve the system of equations

I don't have a problem making them both fractions. I tried to simplify by subtracting 16/7 from 5 and then I divided by -y to make it positive. I guess that was incorrect.

How should I proceed?

#### Denis

##### Senior Member
Re: solve the system of equations

bethany3168 said:
I don't have a problem making them both fractions. I tried to simplify by subtracting 16/7 from 5 and then I divided by -y to make it positive. I guess that was incorrect.
How should I proceed?
You should proceed by going back to beginning; you have:
2x – y = 5
3x + 2y = 2
2x-y=5
-2x -2x
y=-2x+5

That should be y = 2x - 5

G

#### Guest

##### Guest
solve the system of equations

But I have to solve for y with a number and then check the number solutions to make sure they work. ?

#### Denis

##### Senior Member
Geezzz Bethany, do you or do you not understand?
2x – y = 5 [1]
3x + 2y = 2 [2]

[1]: y = 2x - 5

Substitute that in [2]:
3x + 2(2x - 5) = 2
3x + 2x - 10 = 2
5x = 12
x = 12/5

Substitute that in [1]:
2(12/5) - y = 5
24/5 - y = 5
y = 24/5 - 5
y = 24/5 - 25/5
y = -1/5

[1] says that 2x - y = 5
let's see:
2(12/5) - (-1/5)
= 24/5 + 1/5
= 25/5
= 5 : Bingo! OK??????????????????????????

G

#### Guest

##### Guest
solve the system of equations

I guess I don't understand. Sorry. Math does not come easily to me. I have to struggle through each problem. I am happy this site is here to offer assistance, I really hate asking for help but I just don't understand.

I don't see how 2x-y=5 is y=2x-5

I subtracted 2x from each side which is what I thought I was suppose to do. By doing that, it makes the 2x negative. Then I have the -y to deal with don't I?

#### stapel

##### Super Moderator
Staff member
After you subtracted 2x from either side, you should have had:

. . . . .-y = -2x + 5

Now multiply through by -1, and you'll get what the tutor showed you.

Eliz.

G

#### Guest

##### Guest
solving the system of equations

Okay, I understand the first equation.

Now, why on the second equation is
3x+2(2x-5)=2 not 3x+4x-10?

The tutor shows it as 3x+2x-10=2

Sorry to be so thickheaded, but if I don't break it down I will never understand it.

#### Denis

##### Senior Member
Re: solving the system of equations

bethany3168 said:
Okay, I understand the first equation.
Now, why on the second equation is
3x+2(2x-5)=2 not 3x+4x-10?
The tutor shows it as 3x+2x-10=2
Sorry to be so thickheaded, but if I don't break it down I will never understand it.
Yaggot me Bethany!
I goofed...you're correct, of course...apologies for confusing you...

Correcting what I did:
Substitute that in [2]:
3x + 2(2x - 5) = 2
3x + 4x - 10 = 2
7x = 12
x = 12/7

Substitute that in [1]:
2(12/7) - y = 5
y = -11/7

[1] says that 2x - y = 5
let's see:
2(12/7) - (-11/7)
= 35/7
= 5 : Bingo! OK??????????????????????????

By the way, another way to handle stuff like:
2x - y = 5 : what is y?

you can move a term from one side of equal sign to the other side
by changing the sign of the term you're moving; like this:

2x = 5 + y : the y is moved, changing sign from - to +

2x - 5 = y : the 5 is moved, changing sign from + to -

A li'l example to convince you:
13 - 6 = 7
13 = 7 + 6
or:
13 + 6 = 19
13 = 19 - 6

Yokay?

Don't let something like "2x" scare you: 2x is simply a number.

G

#### Guest

##### Guest
System of equations

It sure is easy to do isn't it! :wink:

I will forever be grateful to all of you for getting me through this! I apoligize for taking up so much of your time.

Hope you all have a wonderful day.