# Elimination method: 4x - 3y = 17, 10x + y = -4

#### Stine

##### New member
4x - 3y = 17
10x + y = -4

I tried this:

4x - 3y = 17
3(10x + y) = 3(-4)

4x - 3y = 17
30x + 3y = -12

34x = 5

This is not looking good here, at least not to me. Did I do something wrong?

#### tkhunny

##### Moderator
Staff member
Re: Elimination method

Stine said:
3(10x+y)=-4
That is really nasty notation. Please don't do it again. You will confuse everyone, including yourself.

Who said all answers had to be pretty? However, given answers thought to be funky, one might check to see if the problem is copied correctly.

elimination

Ok...

4x-3y=17
10x+y=-4

4x-3y=17
3* (10x+y=-4)

Is this better?

#### stapel

##### Super Moderator
Staff member
Stine said:
34x = 5

This is not looking good here, at least not to me. Did I do something wrong?
Just keep going, and see what you get:

. . . . .x = 5/34

From the second of the original equations:

. . . . .y = -10x - 4

. . . . .y = -10(5/34) - 4

Continue. Then plug your answers (messy or not) back into the original equations, to check if they work.

Eliz.

#### Stine

##### New member
ok not working for me I don't think...

so I have

4(5/34)-3y=17
=10/17-3y=17-10/17

-3y=16 7/17
__ ______
-3 -3

Uuuuuummm? what in the world am I doing wrong???? :? :? :? :wink:

#### Mrspi

##### Senior Member
Stine said:
ok not working for me I don't think...

so I have

4(5/34)-3y=17
=10/17-3y=17-10/17

-3y=16 7/17
__ ______
-3 -3

Uuuuuummm? what in the world am I doing wrong???? :? :? :? :wink:
You might find it easier to write that "16 7/17" as an improper fraction: 279/17

-3y = 279/17

Let's multiply both sides by -1/3....that will accomplish the same thing as dividing by -3:

(-1/3)(-3y) = (-1/3)(279/17)

y = -93/17

Not a nice-looking answer, for sure. But, as was suggested earlier, we can check to see if each equation is true when x = 5/34 and y = -93/17

Substituting into the first equation:
4x - 3y = 17
4(5/34) - 3(-93/17) =? 17

10/17 + 279/17 =? 17

289/17 =? 17

17 = 17
There...the first equation is true.

Substituting into the second equation:

10x + y = -4

10(5/34) + (-93/17) =? -4

(25/17) + (-93/17) =? -4

(-68/17) =? -4

-4 = -4
And the second equation is true, as well.

Just goes to show you that not all correct answers are "nice."

#### Stine

##### New member
Thank you MrsPi- You are right about the not all answers are nice looking numbers... Sweet! Thank you-Thank you! :lol:

#### tkhunny

##### Moderator
Staff member
Re: elimination

Stine said:
4x-3y=17
3* (10x+y=-4)

Is this better?
No. Try English. There is no Distributive Property of Equals. I realize you are trying to invent a useful shorthand. Don't. Please don't invent new notation. There is already way too much.

R1: 4x-3y=17
R2: 10x+y=-4

Multiply R2 by 3, creating a new R2

R1: 4x-3y=17
R2: 30x+3y=-12

Add R1 to R2, creating a new R2

R1: 4x-3y=17
R2: 34x=5

Divide R2 by 34, creating a new R2

R1: 4x-3y=17
R2: x=5/34

Multiply R2 by -4, creating a new R2

R1: 4x-3y=17
R2: -4x=-10/17

Add R2 to R1, creating a new R1

R1: -3y=279/17
R2: -4x=-10/17

Divide R1 by -3 and R2 by -4, giving the final result

R1: y=-93/17
R2: x=5/34