# Thread: Simultaneous Equations sorted not

1. ## Simultaneous Equations sorted not

Just when I thought I was getting somewhere I still just can't quite crack it

I have;

3x + 2y = 3
5x - 1y = - 8

I am asked to solve the equations so this is what I have tried

(3+5)x + (2-1)y = 3 - 8
8x / 8 = - 5 / 8 = x - 0.625

3(-0.625) + 2y = 3
- 1.875 + 2y = 3
2y = 3 = 1.875
2y = 4.88
2y = 4.88
2 2

y = 2.44

Check;

3(-0.625) + 2(2.44) = 3.00

5(-0.625) - 1(2.44) = - 5.57

The latter should be -8?

Anybody see what I am getting wrong?

Thanks

David

2. ## Re: Simultaneous Equations sorted not

Originally Posted by David Green
Just when I thought I was getting somewhere I still just can't quite crack it

I have;

3x + 2y = 3
5x - 1y = - 8
Multiply the second equation by 2.
Solve for x.
Then solve for y.

3. ## Re: Simultaneous Equations sorted not

Originally Posted by Plato
Multiply the second equation by 2.
Solve for x.
Then solve for y.
That method does'nt seem to work?

3x + 2y = 3
5x - 1y = - 8

multiplying the second equation by 2

10x - 2y = - 16
3x + 2y = 3
13x - 0 = - 5.33

x = 0.41

somewhere I am getting it wrong but can't see it?

4. ## Re: Simultaneous Equations sorted not

-16+3=-13 not -5,33 so x=...

5. ## Re: Simultaneous Equations sorted not

Originally Posted by Siron
-16+3=-13 not -5,33 so x=...
OK here goes?

3x + 2y = 3
5x - 1y = - 8

10x + 2y = - 16

3x + 2(10x - 2y) = - 16
3x + 20x - 4y = - 16

the rest of this method I don't think works?

10x - 2y = - 16
3x + 2y = - 16
2y = - 16 + 3
2y = - 13
y = - 6.5

3x + 2 (- 6.5) = 3
3x - 13 = 3
3x = 16

x = 5.33

3(5.33) + 2(-6.5) = 15.99 - 13 = 2.99 almost there?

5(5.33) - 1(-6.5) = 26.65 - 6.5 = 20.15?????? definately not - 8????

6. ## Re: Simultaneous Equations sorted not

What you did in your previous post was fine, by following Plato's hint and multiplying the second equation with 2 and make the addition between the two equations gives:
$13x-0=-13 \Leftrightarrow 13x=-13 \Leftrightarrow x=-1$
Now determine $y$

7. ## Re: Simultaneous Equations sorted not

why are you making this so difficult?

3x + 2y = 3
5x - 1y = - 8

multiply 2nd equation by 2 and add the equations term for term ...

3x + 2y = 3
10x - 2y = -16
-----------------
13x = -13

x = -1

8. ## Re: Simultaneous Equations sorted not

Originally Posted by skeeter
why are you making this so difficult?

3x + 2y = 3
5x - 1y = - 8

multiply 2nd equation by 2 and add the equations term for term ...

3x + 2y = 3
10x - 2y = -16
-----------------
13x = -13

x = -1
It is difficult not to make something hard when one does not know what one is doing?

I'll try again with all the help so far, which I must say thank you to all.

3x + 2y = 3
5x - 1y = - 8

10x - 2y = - 16
3x +2y = 3
13x = - 13

x = - 1

3x + 2y = 3

3(-1) + 2y = 3
-3 + 2y = 3

2y = 3 + 3
y = 3

3x + 2y = 3

3(-1) + 2(3) = -3 + 6 = 3

5x - 1y = - 8

5(-1) - 1(3) = - 5 - 3 = - 8

so x = -1 and y = 3

Thanks all, I am still learning.

Correct!