# Thread: Simultaneous Equations

1. ## Simultaneous Equations

Hi

I am trying to solve the following equation, but I'm not sure if I'm right, can anybody advise?

2x + 3y = 19
6x - 7y = -7

So far I have done the following:

4x + 6y = 38

Added the second and third equation, to get:

10x + 13y = 31

31 / 10 = 3.1
3.1 * 2 = 6.2

19 - 6.2 = 12.8 / 3 = 4.3

x = 3.1
y = 4.3

I appreciate any advice.

2. Originally Posted by Gall1987
Hi

I am trying to solve the following equation, but I'm not sure if I'm right, can anybody advise?

2x + 3y = 19
6x - 7y = -7

So far I have done the following:

4x + 6y = 38

Added the second and third equation, to get:

10x + 13y = 31
The goal of adding two equations is to get one equation in one unknown. I'd recommend multiplying both sides of your first equation by -3, giving
-6x - 9y = -57

Now add that to the second equation. You will have an equation in y only that you can solve.

-Dan

3. Originally Posted by topsquark
The goal of adding two equations is to get one equation in one unknown. I'd recommend multiplying both sides of your first equation by -3, giving
-6x - 9y = -57

Now add that to the second equation. You will have an equation in y only that you can solve.

-Dan
Can you tell me why I need to multiply the first equation by a negative number? I have originally tried the following, but now I'm stuck:

6x + 9y = 57 +6x -7y = -7 = 12x + 2y = 50.

Can you advise me how to resolve it? This is just revision for an upcoming exam, so I just need to know the concept to solve them and I should hopefully then be OK.

4. Originally Posted by Gall1987
Can you tell me why I need to multiply the first equation by a negative number? I have originally tried the following, but now I'm stuck:

6x + 9y = 57 +6x -7y = -7 = 12x + 2y = 50.

Can you advise me how to resolve it? This is just revision for an upcoming exam, so I just need to know the concept to solve them and I should hopefully then be OK.
When you are trying to solve a system of equations the goal is to find some way of writing a single equation in a single unknown. In this case we compare the two equations:
2x + 3y = 19
6x - 7y = -7

We want to get rid of, say, x. So if we multiply the first equation by -3:
-6x + -18y = -57
6x - 7y = -7

And add the two equations:
(-6x + 6x) + (-18y - 7y) = (-57 - 7)

-25y = -64
which you can immediately solve for y.

The other way is to
2x + 3y = 19
6x - 7y = -7

multiply the top equation by 7 and the bottom by 3:
14x + 21y = 133
18x - 21y = -21

(14x + 18x) + (21y - 21y) = (133 - 21)

32x = 112
which you can, again, solve.

-Dan

5. Originally Posted by Gall1987
Can you tell me why I need to multiply the first equation by a negative number? I have originally tried the following, but now I'm stuck:

6x + 9y = 57 +6x -7y = -7 = 12x + 2y = 50.

Can you advise me how to resolve it? This is just revision for an upcoming exam, so I just need to know the concept to solve them and I should hopefully then be OK.
To address your method how did you get
6x + 9y = 57 +6x -7y

-Dan

6. Originally Posted by Gall1987
Hi

Added the second and third equation, to get:

10x + 13y = 31
6x+4x=10x - right
-7+38=31 - right
-7y+6y=-1y and you`ve written 13y

7. Using google can save you lotsa time(!):

8. Originally Posted by Gall1987
Hi

I am trying to solve the following equation, but I'm not sure if I'm right, can anybody advise?

2x + 3y = 19
6x - 7y = -7

So far I have done the following:

4x + 6y = 38
Okay, you multiplied the first equation by 2- any specific reason for doing that?

Added the second and third equation, to get:

10x + 13y = 31
Again, yes, that's true but why did you do that? You still have two unknowns- there are an infinite number of x,y pairs that will satify that equation.

31 / 10 = 3.1
Are you saying that x= 3.1? That would be true if x satisfied 10x= 31 which would be true if y= 0.

3.1 * 2 = 6.2

19 - 6.2 = 12.8 / 3 = 4.3

x = 3.1
y = 4.3
And now you are saying that, with this value of x, y is not 0 so that x= 31/10 was wrong.

I appreciate any advice.
You seem to be just doing things at random. Also, you said "I'm not sure if I'm right". Did you consider checking your answer?
If x= 3.1 and y= 4.3 then 3x+ 3y= 2(3.1)+ 3(4.3)= 6.2+ 12.9= 19.1, not 19. And 6x- 7y= 18.6- 30.1= --11.5 not -7.