You are Here: Home >< Maths

# Simultaneous equations

Announcements Posted on
Last day to win £100 of Amazon vouchers - don't miss out! Take our quick survey to enter 24-10-2016
1. How would I solve this??

3x - 2y = 7
7x + 2y = 13
2. (Original post by Jack_Tomlin)
How would I solve this??

3x - 2y = 7
7x + 2y = 13
What do you think? What can you cancel?
3. (Original post by Jack_Tomlin)
How would I solve this??

3x - 2y = 7
7x + 2y = 13
Notice that the "y"s have the same coefficient though with a different sign (-2 and +2). This means that you can add the equations together:

3x - 2y + 7x + 2y = 7 + 13

Then simplify, and you will find that you are left with an x term and a number.

5x = 20
x = 20/5
x = 4

Then substitute the value x = 4 into the top equation, ie replace the x with a 4.
4. (Original post by OscarTG)
Notice that the "y"s have the same coefficient though with a different sign (-2 and +2). This means that you can add the equations together:

3x - 2y + 7x + 2y = 7 + 13

Then simplify, and you will find that you are left with an x term and a number.

5x = 20
x = 20/5
x = 4

Then substitute the value x = 4 into the top equation, ie replace the x with a 4.
I don't understand why you add the equations together? Would you mind doing a written method?
5. (Original post by Jack_Tomlin)
I don't understand why you add the equations together? Would you mind doing a written method?
-2++2=0

when the signs are different you always add, when they are the same you always subtract
6. (Original post by Jack_Tomlin)
I don't understand why you add the equations together? Would you mind doing a written method?
You add them because then the y's cancel, thus leaving you only with an x which you can solve for. Once you have your x, substitute that into one of the two equations and solve for y.

When solving simultaneous equations you always aim to get rid off either x or y and in this case we choose y because it's easier by having the same coefficient (the number next to it).
7. (Original post by SuperHuman98)
-2++2=0

when the signs are different you always add, when they are the same you always subtract
But I thought these were the rules:

- x - = +
+ x + = +
- X + = -
+ x - = -
8. (Original post by Jack_Tomlin)
But I thought these were the rules:

- x - = +
+ x + = +
- X + = -
+ x - = -
That's when you multiply numbers together... you don't multiply/divide two equations when it comes to solving them here.
9. (Original post by Jack_Tomlin)
How would I solve this??

3x - 2y = 7
7x + 2y = 13
Add them together to get rid of Y so you can solve for x
(Original post by OscarTG)
Notice that the "y"s have the same coefficient though with a different sign (-2 and +2). This means that you can add the equations together:

3x - 2y + 7x + 2y = 7 + 13

Then simplify, and you will find that you are left with an x term and a number.

5x = 20
x = 20/5
x = 4

Then substitute the value x = 4 into the top equation, ie replace the x with a 4.
i though 7x+3x was 10x not 5x???
10. (Original post by Jack_Tomlin)
How would I solve this??

3x - 2y = 7
7x + 2y = 13
eqn1 + eqn 2
10x= 20
x= 2
Sub x = 2 into eqn 1
6 - 2y = 7
2y = -1
y = -0.5

Posted from TSR Mobile
11. (Original post by Jack_Tomlin)
I don't understand why you add the equations together? Would you mind doing a written method?
You have a pair of simultaneous equations with two variables, x and y. The "x"s and "y"s are of the same value in both equations. But in order to obtain any of their values, you need to make an equation with only one variable, x or y, and then solve for that variable. Then substitute that value into one of the original equations.

(3x - 2y = 7)
[7x + 2y = 13]

We have xs and ys. (3x - 2y) is equal to (7), and [7x + 2y] is equal to [13], so:
(3x - 2y) + [7x + 2y] = (7) + [13]

Here everything is being added or subtracted, so we can simply remove the brackets and simplify:

3x + 7x + 2y - 2y = 7 + 13
10x = 20 <---- Indeed, I made a numerical error in my rushed response earlier, my apologies for that.

From that, you can solve the value of x, and substitute that numerical value in the place of x into any of the two original equations, to leave just one variable (y in this case).

I hope I have explained myself well.
12. I have tried to do this one but dont know what to do next:

6x + 2y = 22 (1)
5x + 4y = 23 (2)

First I made the coefficients the same:

6x + 2y = 22 (x 4)
5x + 4y = 23 (x 2)

12x + 8y = 88
10x + 8y = 46
13. (Original post by Jack_Tomlin)
I have tried to do this one but dont know what to do next:

6x + 2y = 22 (1)
5x + 4y = 23 (2)

First I made the coefficients the same:

6x + 2y = 22 (x 4)
5x + 4y = 23 (x 2)

12x + 8y = 88
10x + 8y = 46
Well done, now take one away from the other because if you were to add them, you would end up with 22x+16y=134 which you can't solve on its own. It's really as simple as that. I hope you understand that by combining these two equations through means of subtraction/addition, you can solve for one of the variables which wouldn't be possible given only one of those equations.
14. (Original post by Jack_Tomlin)
How would I solve this??3x - 2y = 77x + 2y = 13
rearrange either of the equations for 2y, then substitute.
15. (Original post by RDKGames)
Well done, now take one away from the other because if you were to add them, you would end up with 22x+16y=134 which you can't solve on its own. It's really as simple as that. I hope you understand that by combining these two equations through means of subtraction/addition, you can solve for one of the variables which wouldn't be possible given only one of those equations.
12x + 8y = 88
10x + 8y = 46

So would it now be 10x = 42

then i would divide by 10 to get x on its own then do the same to 42 and I get x = 4.2
16. (Original post by Jack_Tomlin)
12x + 8y = 88
10x + 8y = 46

So would it now be 10x = 42

then i would divide by 10 to get x on its own then do the same to 42 and I get x = 4.2
No. Where did you get that from?
17. (Original post by RDKGames)
No. Where did you get that from?
I don't know
18. (Original post by Jack_Tomlin)
I don't know
12x + 8y = 88 ... (1)
10x + 8y = 46 ... (2)

Subtract (2) from (1) on both sides.

and you can solve that.
19. this thread is infuriating. Add them together, it's not hard. Watch some tutorial video if you're unsure. x=2 y = -0.5 is the solution

Posted from TSR Mobile
20. (Original post by 98matt)
this thread is infuriating. Add them together, it's not hard. Watch some tutorial video if you're unsure. x=2 y = -0.5 is the solution

Posted from TSR Mobile
I feel the same way lol, but would't want to be rude or anything. I wonder what year OP is in.

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: July 31, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### How does exam reform affect you?

From GCSE to A level, it's all changing

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams